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Simplifying (3x2 + -3)(2x2 + 8) = 0 Reorder the terms: (-3 + 3x2)(2x2 + 8) = 0 Reorder the terms: (-3 + 3x2)(8 + 2x2) = 0 Multiply (-3 + 3x2) * (8 + 2x2) (-3(8 + 2x2) + 3x2 * (8 + 2x2)) = 0 ((8 * -3 + 2x2 * -3) + 3x2 * (8 + 2x2)) = 0 ((-24 + -6x2) + 3x2 * (8 + 2x2)) = 0 (-24 + -6x2 + (8 * 3x2 + 2x2 * 3x2)) = 0 (-24 + -6x2 + (24x2 + 6x4)) = 0 Combine like terms: -6x2 + 24x2 = 18x2 (-24 + 18x2 + 6x4) = 0 Solving -24 + 18x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + 3x2 + x4) = 0 Factor a trinomial. 6((-4 + -1x2)(1 + -1x2)) = 0 Factor a difference between two squares. 6((-4 + -1x2)((1 + x)(1 + -1x))) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve: Simplifying -4 + -1x2 = 0 Solving -4 + -1x2 = 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 + -1x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x2 = 0 + 4 -1x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x2 = 4 Divide each side by '-1'. x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1, 1}
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