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Simplifying (2x + -3)(5x + 1) + (2x + -3)(3x + 4) = 0 Reorder the terms: (-3 + 2x)(5x + 1) + (2x + -3)(3x + 4) = 0 Reorder the terms: (-3 + 2x)(1 + 5x) + (2x + -3)(3x + 4) = 0 Multiply (-3 + 2x) * (1 + 5x) (-3(1 + 5x) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0 ((1 * -3 + 5x * -3) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0 ((-3 + -15x) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0 (-3 + -15x + (1 * 2x + 5x * 2x)) + (2x + -3)(3x + 4) = 0 (-3 + -15x + (2x + 10x2)) + (2x + -3)(3x + 4) = 0 Combine like terms: -15x + 2x = -13x (-3 + -13x + 10x2) + (2x + -3)(3x + 4) = 0 Reorder the terms: -3 + -13x + 10x2 + (-3 + 2x)(3x + 4) = 0 Reorder the terms: -3 + -13x + 10x2 + (-3 + 2x)(4 + 3x) = 0 Multiply (-3 + 2x) * (4 + 3x) -3 + -13x + 10x2 + (-3(4 + 3x) + 2x * (4 + 3x)) = 0 -3 + -13x + 10x2 + ((4 * -3 + 3x * -3) + 2x * (4 + 3x)) = 0 -3 + -13x + 10x2 + ((-12 + -9x) + 2x * (4 + 3x)) = 0 -3 + -13x + 10x2 + (-12 + -9x + (4 * 2x + 3x * 2x)) = 0 -3 + -13x + 10x2 + (-12 + -9x + (8x + 6x2)) = 0 Combine like terms: -9x + 8x = -1x -3 + -13x + 10x2 + (-12 + -1x + 6x2) = 0 Reorder the terms: -3 + -12 + -13x + -1x + 10x2 + 6x2 = 0 Combine like terms: -3 + -12 = -15 -15 + -13x + -1x + 10x2 + 6x2 = 0 Combine like terms: -13x + -1x = -14x -15 + -14x + 10x2 + 6x2 = 0 Combine like terms: 10x2 + 6x2 = 16x2 -15 + -14x + 16x2 = 0 Solving -15 + -14x + 16x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -8x)(3 + -2x) = 0Subproblem 1
Set the factor '(-5 + -8x)' equal to zero and attempt to solve: Simplifying -5 + -8x = 0 Solving -5 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -8x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8x = 0 + 5 -8x = 0 + 5 Combine like terms: 0 + 5 = 5 -8x = 5 Divide each side by '-8'. x = -0.625 Simplifying x = -0.625Subproblem 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 = {-0.625, 1.5}
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