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Simplifying (1 + -1x)(5x + 3) = (3x + -7)(x + -1) Reorder the terms: (1 + -1x)(3 + 5x) = (3x + -7)(x + -1) Multiply (1 + -1x) * (3 + 5x) (1(3 + 5x) + -1x * (3 + 5x)) = (3x + -7)(x + -1) ((3 * 1 + 5x * 1) + -1x * (3 + 5x)) = (3x + -7)(x + -1) ((3 + 5x) + -1x * (3 + 5x)) = (3x + -7)(x + -1) (3 + 5x + (3 * -1x + 5x * -1x)) = (3x + -7)(x + -1) (3 + 5x + (-3x + -5x2)) = (3x + -7)(x + -1) Combine like terms: 5x + -3x = 2x (3 + 2x + -5x2) = (3x + -7)(x + -1) Reorder the terms: 3 + 2x + -5x2 = (-7 + 3x)(x + -1) Reorder the terms: 3 + 2x + -5x2 = (-7 + 3x)(-1 + x) Multiply (-7 + 3x) * (-1 + x) 3 + 2x + -5x2 = (-7(-1 + x) + 3x * (-1 + x)) 3 + 2x + -5x2 = ((-1 * -7 + x * -7) + 3x * (-1 + x)) 3 + 2x + -5x2 = ((7 + -7x) + 3x * (-1 + x)) 3 + 2x + -5x2 = (7 + -7x + (-1 * 3x + x * 3x)) 3 + 2x + -5x2 = (7 + -7x + (-3x + 3x2)) Combine like terms: -7x + -3x = -10x 3 + 2x + -5x2 = (7 + -10x + 3x2) Solving 3 + 2x + -5x2 = 7 + -10x + 3x2 Solving for variable 'x'. Reorder the terms: 3 + -7 + 2x + 10x + -5x2 + -3x2 = 7 + -10x + 3x2 + -7 + 10x + -3x2 Combine like terms: 3 + -7 = -4 -4 + 2x + 10x + -5x2 + -3x2 = 7 + -10x + 3x2 + -7 + 10x + -3x2 Combine like terms: 2x + 10x = 12x -4 + 12x + -5x2 + -3x2 = 7 + -10x + 3x2 + -7 + 10x + -3x2 Combine like terms: -5x2 + -3x2 = -8x2 -4 + 12x + -8x2 = 7 + -10x + 3x2 + -7 + 10x + -3x2 Reorder the terms: -4 + 12x + -8x2 = 7 + -7 + -10x + 10x + 3x2 + -3x2 Combine like terms: 7 + -7 = 0 -4 + 12x + -8x2 = 0 + -10x + 10x + 3x2 + -3x2 -4 + 12x + -8x2 = -10x + 10x + 3x2 + -3x2 Combine like terms: -10x + 10x = 0 -4 + 12x + -8x2 = 0 + 3x2 + -3x2 -4 + 12x + -8x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -4 + 12x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 3x + -2x2) = 0 Factor a trinomial. 4((-1 + x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {1, 0.5}
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