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Simplifying ((3x2) + -3)((3x2) + -3) = 0 Reorder the terms: (-3 + (3x2))((3x2) + -3) = 0 Reorder the terms: (-3 + (3x2))(-3 + (3x2)) = 0 Multiply (-3 + (3x2)) * (-3 + (3x2)) (-3(-3 + (3x2)) + (3x2)(-3 + (3x2))) = 0 ((-3 * -3 + (3x2) * -3) + (3x2)(-3 + (3x2))) = 0 ((9 + -9x2) + (3x2)(-3 + (3x2))) = 0 (9 + -9x2 + (-3 * 3x2 + (3x2) * 3x2)) = 0 (9 + -9x2 + (-9x2 + 9x4)) = 0 Combine like terms: -9x2 + -9x2 = -18x2 (9 + -18x2 + 9x4) = 0 Solving 9 + -18x2 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -2x2 + x4) = 0 Factor a trinomial. 9((1 + -1x2)(1 + -1x2)) = 0 Factor a difference between two squares. 9(((1 + x)(1 + -1x))(1 + -1x2)) = 0 Factor a difference between two squares. 9(((1 + x)(1 + -1x))(1 + x)(1 + -1x)) = 0 Ignore the factor 9.Subproblem 1
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 2
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 = 1Subproblem 3
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 4
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, -1, 1}
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