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Simplifying -12x2 + 21x = 6x2 + 3x Reorder the terms: 21x + -12x2 = 6x2 + 3x Reorder the terms: 21x + -12x2 = 3x + 6x2 Solving 21x + -12x2 = 3x + 6x2 Solving for variable 'x'. Reorder the terms: 21x + -3x + -12x2 + -6x2 = 3x + 6x2 + -3x + -6x2 Combine like terms: 21x + -3x = 18x 18x + -12x2 + -6x2 = 3x + 6x2 + -3x + -6x2 Combine like terms: -12x2 + -6x2 = -18x2 18x + -18x2 = 3x + 6x2 + -3x + -6x2 Reorder the terms: 18x + -18x2 = 3x + -3x + 6x2 + -6x2 Combine like terms: 3x + -3x = 0 18x + -18x2 = 0 + 6x2 + -6x2 18x + -18x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 18x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '18x'. 18x(1 + -1x) = 0 Ignore the factor 18.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1}
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