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Simplifying (2x2 + -8)(3x2 + -48) = 0 Reorder the terms: (-8 + 2x2)(3x2 + -48) = 0 Reorder the terms: (-8 + 2x2)(-48 + 3x2) = 0 Multiply (-8 + 2x2) * (-48 + 3x2) (-8(-48 + 3x2) + 2x2 * (-48 + 3x2)) = 0 ((-48 * -8 + 3x2 * -8) + 2x2 * (-48 + 3x2)) = 0 ((384 + -24x2) + 2x2 * (-48 + 3x2)) = 0 (384 + -24x2 + (-48 * 2x2 + 3x2 * 2x2)) = 0 (384 + -24x2 + (-96x2 + 6x4)) = 0 Combine like terms: -24x2 + -96x2 = -120x2 (384 + -120x2 + 6x4) = 0 Solving 384 + -120x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(64 + -20x2 + x4) = 0 Factor a trinomial. 6((4 + -1x2)(16 + -1x2)) = 0 Factor a difference between two squares. 6(((2 + x)(2 + -1x))(16 + -1x2)) = 0 Factor a difference between two squares. 6(((4 + x)(4 + -1x))(2 + x)(2 + -1x)) = 0 Ignore the factor 6.Subproblem 1
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 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 2, -4, 4}
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