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Simplifying 10x2 + 20x = 12x2 + -60x Reorder the terms: 20x + 10x2 = 12x2 + -60x Reorder the terms: 20x + 10x2 = -60x + 12x2 Solving 20x + 10x2 = -60x + 12x2 Solving for variable 'x'. Reorder the terms: 20x + 60x + 10x2 + -12x2 = -60x + 12x2 + 60x + -12x2 Combine like terms: 20x + 60x = 80x 80x + 10x2 + -12x2 = -60x + 12x2 + 60x + -12x2 Combine like terms: 10x2 + -12x2 = -2x2 80x + -2x2 = -60x + 12x2 + 60x + -12x2 Reorder the terms: 80x + -2x2 = -60x + 60x + 12x2 + -12x2 Combine like terms: -60x + 60x = 0 80x + -2x2 = 0 + 12x2 + -12x2 80x + -2x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 80x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(40 + -1x) = 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 '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Divide each side by '-1'. x = 40 Simplifying x = 40Solution
x = {0, 40}
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