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Simplifying 3x(x + 2) = x(x + 4) Reorder the terms: 3x(2 + x) = x(x + 4) (2 * 3x + x * 3x) = x(x + 4) (6x + 3x2) = x(x + 4) Reorder the terms: 6x + 3x2 = x(4 + x) 6x + 3x2 = (4 * x + x * x) 6x + 3x2 = (4x + x2) Solving 6x + 3x2 = 4x + x2 Solving for variable 'x'. Reorder the terms: 6x + -4x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: 6x + -4x = 2x 2x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 2x + 2x2 = 4x + x2 + -4x + -1x2 Reorder the terms: 2x + 2x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 2x + 2x2 = 0 + x2 + -1x2 2x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, -1}
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