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Simplifying x * 4x = 8x + 12 Reorder the terms for easier multiplication: 4x * x = 8x + 12 Multiply x * x 4x2 = 8x + 12 Reorder the terms: 4x2 = 12 + 8x Solving 4x2 = 12 + 8x Solving for variable 'x'. Reorder the terms: -12 + -8x + 4x2 = 12 + 8x + -12 + -8x Reorder the terms: -12 + -8x + 4x2 = 12 + -12 + 8x + -8x Combine like terms: 12 + -12 = 0 -12 + -8x + 4x2 = 0 + 8x + -8x -12 + -8x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -12 + -8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -2x + x2) = 0 Factor a trinomial. 4((-1 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1, 3}
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