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