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Simplifying (3x + -2)(5x + -1) + -1(3x + -2)(3x + -4) = 0 Reorder the terms: (-2 + 3x)(5x + -1) + -1(3x + -2)(3x + -4) = 0 Reorder the terms: (-2 + 3x)(-1 + 5x) + -1(3x + -2)(3x + -4) = 0 Multiply (-2 + 3x) * (-1 + 5x) (-2(-1 + 5x) + 3x * (-1 + 5x)) + -1(3x + -2)(3x + -4) = 0 ((-1 * -2 + 5x * -2) + 3x * (-1 + 5x)) + -1(3x + -2)(3x + -4) = 0 ((2 + -10x) + 3x * (-1 + 5x)) + -1(3x + -2)(3x + -4) = 0 (2 + -10x + (-1 * 3x + 5x * 3x)) + -1(3x + -2)(3x + -4) = 0 (2 + -10x + (-3x + 15x2)) + -1(3x + -2)(3x + -4) = 0 Combine like terms: -10x + -3x = -13x (2 + -13x + 15x2) + -1(3x + -2)(3x + -4) = 0 Reorder the terms: 2 + -13x + 15x2 + -1(-2 + 3x)(3x + -4) = 0 Reorder the terms: 2 + -13x + 15x2 + -1(-2 + 3x)(-4 + 3x) = 0 Multiply (-2 + 3x) * (-4 + 3x) 2 + -13x + 15x2 + -1(-2(-4 + 3x) + 3x * (-4 + 3x)) = 0 2 + -13x + 15x2 + -1((-4 * -2 + 3x * -2) + 3x * (-4 + 3x)) = 0 2 + -13x + 15x2 + -1((8 + -6x) + 3x * (-4 + 3x)) = 0 2 + -13x + 15x2 + -1(8 + -6x + (-4 * 3x + 3x * 3x)) = 0 2 + -13x + 15x2 + -1(8 + -6x + (-12x + 9x2)) = 0 Combine like terms: -6x + -12x = -18x 2 + -13x + 15x2 + -1(8 + -18x + 9x2) = 0 2 + -13x + 15x2 + (8 * -1 + -18x * -1 + 9x2 * -1) = 0 2 + -13x + 15x2 + (-8 + 18x + -9x2) = 0 Reorder the terms: 2 + -8 + -13x + 18x + 15x2 + -9x2 = 0 Combine like terms: 2 + -8 = -6 -6 + -13x + 18x + 15x2 + -9x2 = 0 Combine like terms: -13x + 18x = 5x -6 + 5x + 15x2 + -9x2 = 0 Combine like terms: 15x2 + -9x2 = 6x2 -6 + 5x + 6x2 = 0 Solving -6 + 5x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(2 + -3x) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-1.5, 0.6666666667}
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