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Simplifying 40x = 30x(x + 2) Reorder the terms: 40x = 30x(2 + x) 40x = (2 * 30x + x * 30x) 40x = (60x + 30x2) Solving 40x = 60x + 30x2 Solving for variable 'x'. Combine like terms: 40x + -60x = -20x -20x + -30x2 = 60x + 30x2 + -60x + -30x2 Reorder the terms: -20x + -30x2 = 60x + -60x + 30x2 + -30x2 Combine like terms: 60x + -60x = 0 -20x + -30x2 = 0 + 30x2 + -30x2 -20x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -20x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-10x'. -10x(2 + 3x) = 0 Ignore the factor -10.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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {0, -0.6666666667}
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