Solve the equation by factoring: 2x^(3)+14x^(2)-36 x=0 Answer: x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from the given cubic equation. The equation is 2x^3 + 14x^2 - 36x = 0. The GCF of the terms 2x^3, 14x^2, and -36x is 2x. So we factor out 2x from each term. 2x(x^2 + 7x - 18) = 0Factor Quadratic: Now we need to factor the quadratic equation x^2 + 7x - 18. We are looking for two numbers that multiply to -18 and add up to 7. The numbers that satisfy these conditions are 9 and -2. So we can write the quadratic as (x + 9)(x - 2).Find Roots: Now we have the factored form of the original equation: 2x(x + 9)(x - 2) = 0 To find the roots, we set each factor equal to zero and solve for x. First, set 2x = 0, which gives us x = 0.Set 1st Factor: Next, set the factor (x + 9) equal to zero: x + 9 = 0 Subtract 9 from both sides to solve for x: x = -9Set 2nd Factor: Finally, set the factor (x - 2) equal to zero: x - 2 = 0 Add 2 to both sides to solve for x: x = 2

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Q. Solve the equation by factoring:

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2 x^{3}+14 x^{2}-36 x=0

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Answer:

x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from the given cubic equation. $\newline$ The equation is $2x^3 + 14x^2 - 36x = 0$ . $\newline$ The GCF of the terms $2x^3$ , $14x^2$ , and $-36x$ is $2x$ . $\newline$ So we factor out $2x$ from each term. $\newline$ $2x(x^2 + 7x - 18) = 0$
Factor Quadratic: Now we need to factor the quadratic equation $x^2 + 7x - 18$ . We are looking for two numbers that multiply to $-18$ and add up to $7$ . The numbers that satisfy these conditions are $9$ and $-2$ . So we can write the quadratic as $(x + 9)(x - 2)$ .
Find Roots: Now we have the factored form of the original equation: $\newline$ $2x(x + 9)(x - 2) = 0$ $\newline$ To find the roots, we set each factor equal to zero and solve for $x$ . $\newline$ First, set $2x = 0$ , which gives us $x = 0$ .
Set $1$ st Factor: Next, set the factor $x + 9$ equal to zero: $\newline$ $x + 9 = 0$ $\newline$ Subtract $9$ from both sides to solve for $x$ : $\newline$ $x = -9$
Set $2$ nd Factor: Finally, set the factor $x - 2$ equal to zero: $\newline$ $x - 2 = 0$ $\newline$ Add $2$ to both sides to solve for $x$ : $\newline$ $x = 2$