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Simplifying (x3 + 6x2)(-4x + -24) = 0 Reorder the terms: (6x2 + x3)(-4x + -24) = 0 Reorder the terms: (6x2 + x3)(-24 + -4x) = 0 Multiply (6x2 + x3) * (-24 + -4x) (6x2 * (-24 + -4x) + x3(-24 + -4x)) = 0 ((-24 * 6x2 + -4x * 6x2) + x3(-24 + -4x)) = 0 ((-144x2 + -24x3) + x3(-24 + -4x)) = 0 (-144x2 + -24x3 + (-24 * x3 + -4x * x3)) = 0 (-144x2 + -24x3 + (-24x3 + -4x4)) = 0 Combine like terms: -24x3 + -24x3 = -48x3 (-144x2 + -48x3 + -4x4) = 0 Solving -144x2 + -48x3 + -4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-4x2'. -4x2(36 + 12x + x2) = 0 Factor a trinomial. -4x2((6 + x)(6 + x)) = 0 Ignore the factor -4.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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {0, -6, -6}
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