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Simplifying 3x(x + -6) = 2x(x + -7) Reorder the terms: 3x(-6 + x) = 2x(x + -7) (-6 * 3x + x * 3x) = 2x(x + -7) (-18x + 3x2) = 2x(x + -7) Reorder the terms: -18x + 3x2 = 2x(-7 + x) -18x + 3x2 = (-7 * 2x + x * 2x) -18x + 3x2 = (-14x + 2x2) Solving -18x + 3x2 = -14x + 2x2 Solving for variable 'x'. Reorder the terms: -18x + 14x + 3x2 + -2x2 = -14x + 2x2 + 14x + -2x2 Combine like terms: -18x + 14x = -4x -4x + 3x2 + -2x2 = -14x + 2x2 + 14x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -4x + 1x2 = -14x + 2x2 + 14x + -2x2 Reorder the terms: -4x + 1x2 = -14x + 14x + 2x2 + -2x2 Combine like terms: -14x + 14x = 0 -4x + 1x2 = 0 + 2x2 + -2x2 -4x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + x) = 0Subproblem 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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