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Simplifying 12x = 4x(3x + -1) Reorder the terms: 12x = 4x(-1 + 3x) 12x = (-1 * 4x + 3x * 4x) 12x = (-4x + 12x2) Solving 12x = -4x + 12x2 Solving for variable 'x'. Combine like terms: 12x + 4x = 16x 16x + -12x2 = -4x + 12x2 + 4x + -12x2 Reorder the terms: 16x + -12x2 = -4x + 4x + 12x2 + -12x2 Combine like terms: -4x + 4x = 0 16x + -12x2 = 0 + 12x2 + -12x2 16x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 16x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(4 + -3x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0, 1.333333333}
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