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Simplifying 6x2 + -6x = 9 + -2x2 Reorder the terms: -6x + 6x2 = 9 + -2x2 Solving -6x + 6x2 = 9 + -2x2 Solving for variable 'x'. Reorder the terms: -9 + -6x + 6x2 + 2x2 = 9 + -2x2 + -9 + 2x2 Combine like terms: 6x2 + 2x2 = 8x2 -9 + -6x + 8x2 = 9 + -2x2 + -9 + 2x2 Reorder the terms: -9 + -6x + 8x2 = 9 + -9 + -2x2 + 2x2 Combine like terms: 9 + -9 = 0 -9 + -6x + 8x2 = 0 + -2x2 + 2x2 -9 + -6x + 8x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -9 + -6x + 8x2 = 0 Factor a trinomial. (-3 + -4x)(3 + -2x) = 0Subproblem 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 + -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 = {-0.75, 1.5}
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