Solve the equation by factoring: 30x^(2)-48 x-3x^(3)=0 Answer: x=

Factor GCF: Given the equation: 30x^(2) - 48x - 3x^(3) = 0 First, we should factor out the greatest common factor (GCF) which is 3x in this case. 3x(10x - 16 - x^2) = 0Rearrange Terms: Now we need to rearrange the terms inside the parentheses to make it easier to factor. 3x(-x^2 + 10x - 16) = 0Factor Quadratic: Next, we factor the quadratic expression inside the parentheses. This is a quadratic in the form of ax^2 + bx + c, where a = -1, b = 10, and c = -16. We are looking for two numbers that multiply to a*c (-1*-16 = 16) and add up to b (10). The numbers that satisfy this are 8 and 2 because 8*2 = 16 and 8+2 = 10. So we can write the quadratic as: -x^2 + 8x + 2x - 16Group Terms: Now we group the terms to factor by grouping. 3x[(-x^2 + 8x) + (2x - 16)] = 0Factor Common Factors: Factor out the common factors from each group. 3x[-x(x - 8) + 2(x - 8)] = 0Set Equations: Now we can see that (x - 8) is a common factor. 3x(x - 8)(-x + 2) = 0Solve for x: We can now set each factor equal to zero to solve for x. 3x = 0 or (x - 8) = 0 or (-x + 2) = 0Solving each equation for x gives us the solutions. For 3x = 0, x = 0. For (x - 8) = 0, x = 8. For (-x + 2) = 0, x = 2.

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Solve the equation by factoring:

30x^(2)-48 x-3x^(3)=0
Answer:
x=

Solve the equation by factoring: $\newline$ $30 x^{2}-48 x-3 x^{3}=0$ $\newline$ Answer: $x=$

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Algebra 2

Solve complex trigonomentric equations

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Q. Solve the equation by factoring:

\newline

30 x^{2}-48 x-3 x^{3}=0

\newline

Answer:

x=

Factor GCF: Given the equation: $30x^{2} - 48x - 3x^{3} = 0$ $\newline$ First, we should factor out the greatest common factor (GCF) which is $3x$ in this case. $\newline$ $3x(10x - 16 - x^2) = 0$
Rearrange Terms: Now we need to rearrange the terms inside the parentheses to make it easier to factor. $\newline$ $3x(-x^2 + 10x - 16) = 0$
Factor Quadratic: Next, we factor the quadratic expression inside the parentheses. This is a quadratic in the form of $ax^2 + bx + c$ , where $a = -1$ , $b = 10$ , and $c = -16$ . We are looking for two numbers that multiply to $a*c$ ( $-1*-16 = 16$ ) and add up to $b$ ( $10$ ). The numbers that satisfy this are $8$ and $2$ because $a = -1$ $0$ and $a = -1$ $1$ . So we can write the quadratic as: $a = -1$ $2$
Group Terms: Now we group the terms to factor by grouping. $3x[(-x^2 + 8x) + (2x - 16)] = 0$
Factor Common Factors: Factor out the common factors from each group. $\newline$ $3x[-x(x - 8) + 2(x - 8)] = 0$
Set Equations: Now we can see that $(x - 8)$ is a common factor. $3x(x - 8)(-x + 2) = 0$
Solve for x: We can now set each factor equal to zero to solve for $x$ . $3x = 0$ or $(x - 8) = 0$ or $(-x + 2) = 0$
Solve for x: We can now set each factor equal to zero to solve for x. $\newline$ $3x = 0$ or $(x - 8) = 0$ or $(-x + 2) = 0$ Solving each equation for x gives us the solutions. $\newline$ For $3x = 0$ , $x = 0$ . $\newline$ For $(x - 8) = 0$ , $x = 8$ . $\newline$ For $(-x + 2) = 0$ , $x = 2$ .