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Simplifying (12x4 + -1x2) + -1(8x4 + 3x2) = 0 Reorder the terms: (-1x2 + 12x4) + -1(8x4 + 3x2) = 0 Remove parenthesis around (-1x2 + 12x4) -1x2 + 12x4 + -1(8x4 + 3x2) = 0 Reorder the terms: -1x2 + 12x4 + -1(3x2 + 8x4) = 0 -1x2 + 12x4 + (3x2 * -1 + 8x4 * -1) = 0 -1x2 + 12x4 + (-3x2 + -8x4) = 0 Reorder the terms: -1x2 + -3x2 + 12x4 + -8x4 = 0 Combine like terms: -1x2 + -3x2 = -4x2 -4x2 + 12x4 + -8x4 = 0 Combine like terms: 12x4 + -8x4 = 4x4 -4x2 + 4x4 = 0 Solving -4x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-1 + x2) = 0 Factor a difference between two squares. 4x2((1 + x)(-1 + 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 '(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 + 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 = 1Solution
x = {0, -1, 1}
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