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Simplifying 6x2 + -5x + -6 = 3 + -2x Reorder the terms: -6 + -5x + 6x2 = 3 + -2x Solving -6 + -5x + 6x2 = 3 + -2x Solving for variable 'x'. Reorder the terms: -6 + -3 + -5x + 2x + 6x2 = 3 + -2x + -3 + 2x Combine like terms: -6 + -3 = -9 -9 + -5x + 2x + 6x2 = 3 + -2x + -3 + 2x Combine like terms: -5x + 2x = -3x -9 + -3x + 6x2 = 3 + -2x + -3 + 2x Reorder the terms: -9 + -3x + 6x2 = 3 + -3 + -2x + 2x Combine like terms: 3 + -3 = 0 -9 + -3x + 6x2 = 0 + -2x + 2x -9 + -3x + 6x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -9 + -3x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1x + 2x2) = 0 Factor a trinomial. 3((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1, 1.5}
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