Solve the equation by factoring: 8x+6x^(2)-2x^(3)=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation 8x + 6x^2 - 2x^3 = 0. The GCF of the terms is 2x, so we factor it out. 2x(4 + 3x - x^2) = 0Rearrange Terms: Rearrange the terms inside the parentheses in descending order of the powers of x. 2x(-x^2 + 3x + 4) = 0Factor Quadratic: Factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to -4 (the product of the coefficient of x^2, which is -1, and the constant term, which is 4) and add up to 3 (the coefficient of x). The numbers that satisfy these conditions are 4 and -1. So, we can factor the quadratic as follows: 2x(-(x - 4)(x + 1)) = 0Set Equations: Set each factor equal to zero and solve for x. We have three factors: 2x, -(x - 4), and (x + 1). Setting each factor to zero gives us the equations: 2x = 0 -(x - 4) = 0 x + 1 = 0Solve for x: Solve each equation for x. From 2x = 0, we get x = 0. From -(x - 4) = 0, we get x = 4. From x + 1 = 0, we get x = -1.

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Algebra 2

Quadratic equation with complex roots

Full solution

Q. Solve the equation by factoring:

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8 x+6 x^{2}-2 x^{3}=0

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Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation $8x + 6x^2 - 2x^3 = 0$ . The GCF of the terms is $2x$ , so we factor it out. $2x(4 + 3x - x^2) = 0$
Rearrange Terms: Rearrange the terms inside the parentheses in descending order of the powers of $x$ . $2x(-x^2 + 3x + 4) = 0$
Factor Quadratic: Factor the quadratic expression inside the parentheses. $\newline$ We are looking for two numbers that multiply to $-4$ (the product of the coefficient of $x^2$ , which is $-1$ , and the constant term, which is $4$ ) and add up to $3$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $4$ and $-1$ . $\newline$ So, we can factor the quadratic as follows: $\newline$ $2x(-((x - 4)(x + 1))) = 0$
Set Equations: Set each factor equal to zero and solve for $x$ . We have three factors: $2x$ , $-\left(x - 4\right)$ , and $\left(x + 1\right)$ . Setting each factor to zero gives us the equations: $2x = 0$ $-\left(x - 4\right) = 0$ $x + 1 = 0$
Solve for x: Solve each equation for x. $\newline$ From $2x = 0$ , we get $x = 0$ . $\newline$ From $-(x - 4) = 0$ , we get $x = 4$ . $\newline$ From $x + 1 = 0$ , we get $x = -1$ .