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Simplifying 12x2 = 45x + -27 Reorder the terms: 12x2 = -27 + 45x Solving 12x2 = -27 + 45x Solving for variable 'x'. Reorder the terms: 27 + -45x + 12x2 = -27 + 45x + 27 + -45x Reorder the terms: 27 + -45x + 12x2 = -27 + 27 + 45x + -45x Combine like terms: -27 + 27 = 0 27 + -45x + 12x2 = 0 + 45x + -45x 27 + -45x + 12x2 = 45x + -45x Combine like terms: 45x + -45x = 0 27 + -45x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -15x + 4x2) = 0 Factor a trinomial. 3((3 + -4x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0.75, 3}
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