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Simplifying (2x + 5)(x + -3) + (1 + 4x)(3 + -1x) = 0 Reorder the terms: (5 + 2x)(x + -3) + (1 + 4x)(3 + -1x) = 0 Reorder the terms: (5 + 2x)(-3 + x) + (1 + 4x)(3 + -1x) = 0 Multiply (5 + 2x) * (-3 + x) (5(-3 + x) + 2x * (-3 + x)) + (1 + 4x)(3 + -1x) = 0 ((-3 * 5 + x * 5) + 2x * (-3 + x)) + (1 + 4x)(3 + -1x) = 0 ((-15 + 5x) + 2x * (-3 + x)) + (1 + 4x)(3 + -1x) = 0 (-15 + 5x + (-3 * 2x + x * 2x)) + (1 + 4x)(3 + -1x) = 0 (-15 + 5x + (-6x + 2x2)) + (1 + 4x)(3 + -1x) = 0 Combine like terms: 5x + -6x = -1x (-15 + -1x + 2x2) + (1 + 4x)(3 + -1x) = 0 Multiply (1 + 4x) * (3 + -1x) -15 + -1x + 2x2 + (1(3 + -1x) + 4x * (3 + -1x)) = 0 -15 + -1x + 2x2 + ((3 * 1 + -1x * 1) + 4x * (3 + -1x)) = 0 -15 + -1x + 2x2 + ((3 + -1x) + 4x * (3 + -1x)) = 0 -15 + -1x + 2x2 + (3 + -1x + (3 * 4x + -1x * 4x)) = 0 -15 + -1x + 2x2 + (3 + -1x + (12x + -4x2)) = 0 Combine like terms: -1x + 12x = 11x -15 + -1x + 2x2 + (3 + 11x + -4x2) = 0 Reorder the terms: -15 + 3 + -1x + 11x + 2x2 + -4x2 = 0 Combine like terms: -15 + 3 = -12 -12 + -1x + 11x + 2x2 + -4x2 = 0 Combine like terms: -1x + 11x = 10x -12 + 10x + 2x2 + -4x2 = 0 Combine like terms: 2x2 + -4x2 = -2x2 -12 + 10x + -2x2 = 0 Solving -12 + 10x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 5x + -1x2) = 0 Factor a trinomial. 2((-3 + x)(2 + -1x)) = 0 Ignore the factor 2.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {3, 2}
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