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Simplifying (3x + -1)(4x + 3) + (2x + 5)(x + -3) = 0 Reorder the terms: (-1 + 3x)(4x + 3) + (2x + 5)(x + -3) = 0 Reorder the terms: (-1 + 3x)(3 + 4x) + (2x + 5)(x + -3) = 0 Multiply (-1 + 3x) * (3 + 4x) (-1(3 + 4x) + 3x * (3 + 4x)) + (2x + 5)(x + -3) = 0 ((3 * -1 + 4x * -1) + 3x * (3 + 4x)) + (2x + 5)(x + -3) = 0 ((-3 + -4x) + 3x * (3 + 4x)) + (2x + 5)(x + -3) = 0 (-3 + -4x + (3 * 3x + 4x * 3x)) + (2x + 5)(x + -3) = 0 (-3 + -4x + (9x + 12x2)) + (2x + 5)(x + -3) = 0 Combine like terms: -4x + 9x = 5x (-3 + 5x + 12x2) + (2x + 5)(x + -3) = 0 Reorder the terms: -3 + 5x + 12x2 + (5 + 2x)(x + -3) = 0 Reorder the terms: -3 + 5x + 12x2 + (5 + 2x)(-3 + x) = 0 Multiply (5 + 2x) * (-3 + x) -3 + 5x + 12x2 + (5(-3 + x) + 2x * (-3 + x)) = 0 -3 + 5x + 12x2 + ((-3 * 5 + x * 5) + 2x * (-3 + x)) = 0 -3 + 5x + 12x2 + ((-15 + 5x) + 2x * (-3 + x)) = 0 -3 + 5x + 12x2 + (-15 + 5x + (-3 * 2x + x * 2x)) = 0 -3 + 5x + 12x2 + (-15 + 5x + (-6x + 2x2)) = 0 Combine like terms: 5x + -6x = -1x -3 + 5x + 12x2 + (-15 + -1x + 2x2) = 0 Reorder the terms: -3 + -15 + 5x + -1x + 12x2 + 2x2 = 0 Combine like terms: -3 + -15 = -18 -18 + 5x + -1x + 12x2 + 2x2 = 0 Combine like terms: 5x + -1x = 4x -18 + 4x + 12x2 + 2x2 = 0 Combine like terms: 12x2 + 2x2 = 14x2 -18 + 4x + 14x2 = 0 Solving -18 + 4x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 2x + 7x2) = 0 Factor a trinomial. 2((-9 + -7x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -7x)' equal to zero and attempt to solve: Simplifying -9 + -7x = 0 Solving -9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -7x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7x = 0 + 9 -7x = 0 + 9 Combine like terms: 0 + 9 = 9 -7x = 9 Divide each side by '-7'. x = -1.285714286 Simplifying x = -1.285714286Subproblem 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 = {-1.285714286, 1}
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