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Simplifying 3x(x + 5) = 2x(x + 7) Reorder the terms: 3x(5 + x) = 2x(x + 7) (5 * 3x + x * 3x) = 2x(x + 7) (15x + 3x2) = 2x(x + 7) Reorder the terms: 15x + 3x2 = 2x(7 + x) 15x + 3x2 = (7 * 2x + x * 2x) 15x + 3x2 = (14x + 2x2) Solving 15x + 3x2 = 14x + 2x2 Solving for variable 'x'. Reorder the terms: 15x + -14x + 3x2 + -2x2 = 14x + 2x2 + -14x + -2x2 Combine like terms: 15x + -14x = 1x 1x + 3x2 + -2x2 = 14x + 2x2 + -14x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 1x + 1x2 = 14x + 2x2 + -14x + -2x2 Reorder the terms: 1x + 1x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 1x + 1x2 = 0 + 2x2 + -2x2 1x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 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 '(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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