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Simplifying 2x(x2 + -36)(x2 + 16) = 0 Reorder the terms: 2x(-36 + x2)(x2 + 16) = 0 Reorder the terms: 2x(-36 + x2)(16 + x2) = 0 Multiply (-36 + x2) * (16 + x2) 2x(-36(16 + x2) + x2(16 + x2)) = 0 2x((16 * -36 + x2 * -36) + x2(16 + x2)) = 0 2x((-576 + -36x2) + x2(16 + x2)) = 0 2x(-576 + -36x2 + (16 * x2 + x2 * x2)) = 0 2x(-576 + -36x2 + (16x2 + x4)) = 0 Combine like terms: -36x2 + 16x2 = -20x2 2x(-576 + -20x2 + x4) = 0 (-576 * 2x + -20x2 * 2x + x4 * 2x) = 0 (-1152x + -40x3 + 2x5) = 0 Solving -1152x + -40x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-576 + -20x2 + x4) = 0 Factor a trinomial. 2x((-16 + -1x2)(36 + -1x2)) = 0 Factor a difference between two squares. 2x((-16 + -1x2)((6 + x)(6 + -1x))) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-16 + -1x2)' equal to zero and attempt to solve: Simplifying -16 + -1x2 = 0 Solving -16 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x2 = 0 + 16 -1x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1x2 = 16 Divide each side by '-1'. x2 = -16 Simplifying x2 = -16 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 = -6Subproblem 4
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, -6, 6}
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