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Simplifying (2x + 3)(3x + -4) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: (3 + 2x)(3x + -4) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: (3 + 2x)(-4 + 3x) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Multiply (3 + 2x) * (-4 + 3x) (3(-4 + 3x) + 2x * (-4 + 3x)) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 ((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 ((-12 + 9x) + 2x * (-4 + 3x)) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 (-12 + 9x + (-4 * 2x + 3x * 2x)) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 (-12 + 9x + (-8x + 6x2)) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Combine like terms: 9x + -8x = 1x (-12 + 1x + 6x2) + -1(5x + -2)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: -12 + 1x + 6x2 + -1(-2 + 5x)(2x + -9) = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: -12 + 1x + 6x2 + -1(-2 + 5x)(-9 + 2x) = (x + -1)(3x + 9) + 2x + 42 Multiply (-2 + 5x) * (-9 + 2x) -12 + 1x + 6x2 + -1(-2(-9 + 2x) + 5x * (-9 + 2x)) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + -1((-9 * -2 + 2x * -2) + 5x * (-9 + 2x)) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + -1((18 + -4x) + 5x * (-9 + 2x)) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + -1(18 + -4x + (-9 * 5x + 2x * 5x)) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + -1(18 + -4x + (-45x + 10x2)) = (x + -1)(3x + 9) + 2x + 42 Combine like terms: -4x + -45x = -49x -12 + 1x + 6x2 + -1(18 + -49x + 10x2) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + (18 * -1 + -49x * -1 + 10x2 * -1) = (x + -1)(3x + 9) + 2x + 42 -12 + 1x + 6x2 + (-18 + 49x + -10x2) = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: -12 + -18 + 1x + 49x + 6x2 + -10x2 = (x + -1)(3x + 9) + 2x + 42 Combine like terms: -12 + -18 = -30 -30 + 1x + 49x + 6x2 + -10x2 = (x + -1)(3x + 9) + 2x + 42 Combine like terms: 1x + 49x = 50x -30 + 50x + 6x2 + -10x2 = (x + -1)(3x + 9) + 2x + 42 Combine like terms: 6x2 + -10x2 = -4x2 -30 + 50x + -4x2 = (x + -1)(3x + 9) + 2x + 42 Reorder the terms: -30 + 50x + -4x2 = (-1 + x)(3x + 9) + 2x + 42 Reorder the terms: -30 + 50x + -4x2 = (-1 + x)(9 + 3x) + 2x + 42 Multiply (-1 + x) * (9 + 3x) -30 + 50x + -4x2 = (-1(9 + 3x) + x(9 + 3x)) + 2x + 42 -30 + 50x + -4x2 = ((9 * -1 + 3x * -1) + x(9 + 3x)) + 2x + 42 -30 + 50x + -4x2 = ((-9 + -3x) + x(9 + 3x)) + 2x + 42 -30 + 50x + -4x2 = (-9 + -3x + (9 * x + 3x * x)) + 2x + 42 -30 + 50x + -4x2 = (-9 + -3x + (9x + 3x2)) + 2x + 42 Combine like terms: -3x + 9x = 6x -30 + 50x + -4x2 = (-9 + 6x + 3x2) + 2x + 42 Reorder the terms: -30 + 50x + -4x2 = -9 + 42 + 6x + 2x + 3x2 Combine like terms: -9 + 42 = 33 -30 + 50x + -4x2 = 33 + 6x + 2x + 3x2 Combine like terms: 6x + 2x = 8x -30 + 50x + -4x2 = 33 + 8x + 3x2 Solving -30 + 50x + -4x2 = 33 + 8x + 3x2 Solving for variable 'x'. Reorder the terms: -30 + -33 + 50x + -8x + -4x2 + -3x2 = 33 + 8x + 3x2 + -33 + -8x + -3x2 Combine like terms: -30 + -33 = -63 -63 + 50x + -8x + -4x2 + -3x2 = 33 + 8x + 3x2 + -33 + -8x + -3x2 Combine like terms: 50x + -8x = 42x -63 + 42x + -4x2 + -3x2 = 33 + 8x + 3x2 + -33 + -8x + -3x2 Combine like terms: -4x2 + -3x2 = -7x2 -63 + 42x + -7x2 = 33 + 8x + 3x2 + -33 + -8x + -3x2 Reorder the terms: -63 + 42x + -7x2 = 33 + -33 + 8x + -8x + 3x2 + -3x2 Combine like terms: 33 + -33 = 0 -63 + 42x + -7x2 = 0 + 8x + -8x + 3x2 + -3x2 -63 + 42x + -7x2 = 8x + -8x + 3x2 + -3x2 Combine like terms: 8x + -8x = 0 -63 + 42x + -7x2 = 0 + 3x2 + -3x2 -63 + 42x + -7x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -63 + 42x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-9 + 6x + -1x2) = 0 Factor a trinomial. 7((-3 + x)(3 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {3, 3}
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