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Simplifying (2x + -3)(x + 1) + (2x + -3)(3x + -4) = 0 Reorder the terms: (-3 + 2x)(x + 1) + (2x + -3)(3x + -4) = 0 Reorder the terms: (-3 + 2x)(1 + x) + (2x + -3)(3x + -4) = 0 Multiply (-3 + 2x) * (1 + x) (-3(1 + x) + 2x * (1 + x)) + (2x + -3)(3x + -4) = 0 ((1 * -3 + x * -3) + 2x * (1 + x)) + (2x + -3)(3x + -4) = 0 ((-3 + -3x) + 2x * (1 + x)) + (2x + -3)(3x + -4) = 0 (-3 + -3x + (1 * 2x + x * 2x)) + (2x + -3)(3x + -4) = 0 (-3 + -3x + (2x + 2x2)) + (2x + -3)(3x + -4) = 0 Combine like terms: -3x + 2x = -1x (-3 + -1x + 2x2) + (2x + -3)(3x + -4) = 0 Reorder the terms: -3 + -1x + 2x2 + (-3 + 2x)(3x + -4) = 0 Reorder the terms: -3 + -1x + 2x2 + (-3 + 2x)(-4 + 3x) = 0 Multiply (-3 + 2x) * (-4 + 3x) -3 + -1x + 2x2 + (-3(-4 + 3x) + 2x * (-4 + 3x)) = 0 -3 + -1x + 2x2 + ((-4 * -3 + 3x * -3) + 2x * (-4 + 3x)) = 0 -3 + -1x + 2x2 + ((12 + -9x) + 2x * (-4 + 3x)) = 0 -3 + -1x + 2x2 + (12 + -9x + (-4 * 2x + 3x * 2x)) = 0 -3 + -1x + 2x2 + (12 + -9x + (-8x + 6x2)) = 0 Combine like terms: -9x + -8x = -17x -3 + -1x + 2x2 + (12 + -17x + 6x2) = 0 Reorder the terms: -3 + 12 + -1x + -17x + 2x2 + 6x2 = 0 Combine like terms: -3 + 12 = 9 9 + -1x + -17x + 2x2 + 6x2 = 0 Combine like terms: -1x + -17x = -18x 9 + -18x + 2x2 + 6x2 = 0 Combine like terms: 2x2 + 6x2 = 8x2 9 + -18x + 8x2 = 0 Solving 9 + -18x + 8x2 = 0 Solving for variable 'x'. 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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