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Simplifying (x3 + 2x2)(-36x + -72) = 0 Reorder the terms: (2x2 + x3)(-36x + -72) = 0 Reorder the terms: (2x2 + x3)(-72 + -36x) = 0 Multiply (2x2 + x3) * (-72 + -36x) (2x2 * (-72 + -36x) + x3(-72 + -36x)) = 0 ((-72 * 2x2 + -36x * 2x2) + x3(-72 + -36x)) = 0 ((-144x2 + -72x3) + x3(-72 + -36x)) = 0 (-144x2 + -72x3 + (-72 * x3 + -36x * x3)) = 0 (-144x2 + -72x3 + (-72x3 + -36x4)) = 0 Combine like terms: -72x3 + -72x3 = -144x3 (-144x2 + -144x3 + -36x4) = 0 Solving -144x2 + -144x3 + -36x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-36x2'. -36x2(4 + 4x + x2) = 0 Factor a trinomial. -36x2((2 + x)(2 + x)) = 0 Ignore the factor -36.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, -2, -2}
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