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Simplifying x3 + -12x2 + -20x = [-1x3 + 12x2 + -20x] Reorder the terms: -20x + -12x2 + x3 = [-1x3 + 12x2 + -20x] Reorder the terms: -20x + -12x2 + x3 = [-20x + 12x2 + -1x3] Remove brackets around [-20x + 12x2 + -1x3] -20x + -12x2 + x3 = -20x + 12x2 + -1x3 Add '20x' to each side of the equation. -20x + -12x2 + 20x + x3 = -20x + 12x2 + 20x + -1x3 Reorder the terms: -20x + 20x + -12x2 + x3 = -20x + 12x2 + 20x + -1x3 Combine like terms: -20x + 20x = 0 0 + -12x2 + x3 = -20x + 12x2 + 20x + -1x3 -12x2 + x3 = -20x + 12x2 + 20x + -1x3 Reorder the terms: -12x2 + x3 = -20x + 20x + 12x2 + -1x3 Combine like terms: -20x + 20x = 0 -12x2 + x3 = 0 + 12x2 + -1x3 -12x2 + x3 = 12x2 + -1x3 Solving -12x2 + x3 = 12x2 + -1x3 Solving for variable 'x'. Reorder the terms: -12x2 + -12x2 + x3 + x3 = 12x2 + -1x3 + -12x2 + x3 Combine like terms: -12x2 + -12x2 = -24x2 -24x2 + x3 + x3 = 12x2 + -1x3 + -12x2 + x3 Combine like terms: x3 + x3 = 2x3 -24x2 + 2x3 = 12x2 + -1x3 + -12x2 + x3 Reorder the terms: -24x2 + 2x3 = 12x2 + -12x2 + -1x3 + x3 Combine like terms: 12x2 + -12x2 = 0 -24x2 + 2x3 = 0 + -1x3 + x3 -24x2 + 2x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -24x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-12 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Solution
x = {0, 12}
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