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Simplifying -16x2 + 32x = 12 Reorder the terms: 32x + -16x2 = 12 Solving 32x + -16x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 32x + -16x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 32x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 8x + -4x2) = 0 Factor a trinomial. 4((-3 + 2x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {1.5, 0.5}
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