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Simplifying 12x2 + -20x + 4 = 6x + 14 Reorder the terms: 4 + -20x + 12x2 = 6x + 14 Reorder the terms: 4 + -20x + 12x2 = 14 + 6x Solving 4 + -20x + 12x2 = 14 + 6x Solving for variable 'x'. Reorder the terms: 4 + -14 + -20x + -6x + 12x2 = 14 + 6x + -14 + -6x Combine like terms: 4 + -14 = -10 -10 + -20x + -6x + 12x2 = 14 + 6x + -14 + -6x Combine like terms: -20x + -6x = -26x -10 + -26x + 12x2 = 14 + 6x + -14 + -6x Reorder the terms: -10 + -26x + 12x2 = 14 + -14 + 6x + -6x Combine like terms: 14 + -14 = 0 -10 + -26x + 12x2 = 0 + 6x + -6x -10 + -26x + 12x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -10 + -26x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -13x + 6x2) = 0 Factor a trinomial. 2((-1 + -3x)(5 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-0.3333333333, 2.5}
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