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Simplifying 4x(x + 3) = 9x(x + -2) Reorder the terms: 4x(3 + x) = 9x(x + -2) (3 * 4x + x * 4x) = 9x(x + -2) (12x + 4x2) = 9x(x + -2) Reorder the terms: 12x + 4x2 = 9x(-2 + x) 12x + 4x2 = (-2 * 9x + x * 9x) 12x + 4x2 = (-18x + 9x2) Solving 12x + 4x2 = -18x + 9x2 Solving for variable 'x'. Reorder the terms: 12x + 18x + 4x2 + -9x2 = -18x + 9x2 + 18x + -9x2 Combine like terms: 12x + 18x = 30x 30x + 4x2 + -9x2 = -18x + 9x2 + 18x + -9x2 Combine like terms: 4x2 + -9x2 = -5x2 30x + -5x2 = -18x + 9x2 + 18x + -9x2 Reorder the terms: 30x + -5x2 = -18x + 18x + 9x2 + -9x2 Combine like terms: -18x + 18x = 0 30x + -5x2 = 0 + 9x2 + -9x2 30x + -5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 30x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(6 + -1x) = 0 Ignore the factor 5.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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 6}
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