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Simplifying (2x + 3)(x + -4) + (2x + 3)(x + -6) = 0 Reorder the terms: (3 + 2x)(x + -4) + (2x + 3)(x + -6) = 0 Reorder the terms: (3 + 2x)(-4 + x) + (2x + 3)(x + -6) = 0 Multiply (3 + 2x) * (-4 + x) (3(-4 + x) + 2x * (-4 + x)) + (2x + 3)(x + -6) = 0 ((-4 * 3 + x * 3) + 2x * (-4 + x)) + (2x + 3)(x + -6) = 0 ((-12 + 3x) + 2x * (-4 + x)) + (2x + 3)(x + -6) = 0 (-12 + 3x + (-4 * 2x + x * 2x)) + (2x + 3)(x + -6) = 0 (-12 + 3x + (-8x + 2x2)) + (2x + 3)(x + -6) = 0 Combine like terms: 3x + -8x = -5x (-12 + -5x + 2x2) + (2x + 3)(x + -6) = 0 Reorder the terms: -12 + -5x + 2x2 + (3 + 2x)(x + -6) = 0 Reorder the terms: -12 + -5x + 2x2 + (3 + 2x)(-6 + x) = 0 Multiply (3 + 2x) * (-6 + x) -12 + -5x + 2x2 + (3(-6 + x) + 2x * (-6 + x)) = 0 -12 + -5x + 2x2 + ((-6 * 3 + x * 3) + 2x * (-6 + x)) = 0 -12 + -5x + 2x2 + ((-18 + 3x) + 2x * (-6 + x)) = 0 -12 + -5x + 2x2 + (-18 + 3x + (-6 * 2x + x * 2x)) = 0 -12 + -5x + 2x2 + (-18 + 3x + (-12x + 2x2)) = 0 Combine like terms: 3x + -12x = -9x -12 + -5x + 2x2 + (-18 + -9x + 2x2) = 0 Reorder the terms: -12 + -18 + -5x + -9x + 2x2 + 2x2 = 0 Combine like terms: -12 + -18 = -30 -30 + -5x + -9x + 2x2 + 2x2 = 0 Combine like terms: -5x + -9x = -14x -30 + -14x + 2x2 + 2x2 = 0 Combine like terms: 2x2 + 2x2 = 4x2 -30 + -14x + 4x2 = 0 Solving -30 + -14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -7x + 2x2) = 0 Factor a trinomial. 2((-3 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-1.5, 5}
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