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Simplifying x(12x + 2) = 10x(x + 1) Reorder the terms: x(2 + 12x) = 10x(x + 1) (2 * x + 12x * x) = 10x(x + 1) (2x + 12x2) = 10x(x + 1) Reorder the terms: 2x + 12x2 = 10x(1 + x) 2x + 12x2 = (1 * 10x + x * 10x) 2x + 12x2 = (10x + 10x2) Solving 2x + 12x2 = 10x + 10x2 Solving for variable 'x'. Reorder the terms: 2x + -10x + 12x2 + -10x2 = 10x + 10x2 + -10x + -10x2 Combine like terms: 2x + -10x = -8x -8x + 12x2 + -10x2 = 10x + 10x2 + -10x + -10x2 Combine like terms: 12x2 + -10x2 = 2x2 -8x + 2x2 = 10x + 10x2 + -10x + -10x2 Reorder the terms: -8x + 2x2 = 10x + -10x + 10x2 + -10x2 Combine like terms: 10x + -10x = 0 -8x + 2x2 = 0 + 10x2 + -10x2 -8x + 2x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-4 + x) = 0 Ignore the factor 2.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 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Solution
x = {0, 4}
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