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Simplifying (5x + -6)(x + -1) + -1(2x2 + -5x + 3) = 0 Reorder the terms: (-6 + 5x)(x + -1) + -1(2x2 + -5x + 3) = 0 Reorder the terms: (-6 + 5x)(-1 + x) + -1(2x2 + -5x + 3) = 0 Multiply (-6 + 5x) * (-1 + x) (-6(-1 + x) + 5x * (-1 + x)) + -1(2x2 + -5x + 3) = 0 ((-1 * -6 + x * -6) + 5x * (-1 + x)) + -1(2x2 + -5x + 3) = 0 ((6 + -6x) + 5x * (-1 + x)) + -1(2x2 + -5x + 3) = 0 (6 + -6x + (-1 * 5x + x * 5x)) + -1(2x2 + -5x + 3) = 0 (6 + -6x + (-5x + 5x2)) + -1(2x2 + -5x + 3) = 0 Combine like terms: -6x + -5x = -11x (6 + -11x + 5x2) + -1(2x2 + -5x + 3) = 0 Reorder the terms: 6 + -11x + 5x2 + -1(3 + -5x + 2x2) = 0 6 + -11x + 5x2 + (3 * -1 + -5x * -1 + 2x2 * -1) = 0 6 + -11x + 5x2 + (-3 + 5x + -2x2) = 0 Reorder the terms: 6 + -3 + -11x + 5x + 5x2 + -2x2 = 0 Combine like terms: 6 + -3 = 3 3 + -11x + 5x + 5x2 + -2x2 = 0 Combine like terms: -11x + 5x = -6x 3 + -6x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 3 + -6x + 3x2 = 0 Solving 3 + -6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -2x + x2) = 0 Factor a trinomial. 3((1 + -1x)(1 + -1x)) = 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 '(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 = {1, 1}
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