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Simplifying (3x + -4)(x + 5) = (x + 1)(1 + -4x) Reorder the terms: (-4 + 3x)(x + 5) = (x + 1)(1 + -4x) Reorder the terms: (-4 + 3x)(5 + x) = (x + 1)(1 + -4x) Multiply (-4 + 3x) * (5 + x) (-4(5 + x) + 3x * (5 + x)) = (x + 1)(1 + -4x) ((5 * -4 + x * -4) + 3x * (5 + x)) = (x + 1)(1 + -4x) ((-20 + -4x) + 3x * (5 + x)) = (x + 1)(1 + -4x) (-20 + -4x + (5 * 3x + x * 3x)) = (x + 1)(1 + -4x) (-20 + -4x + (15x + 3x2)) = (x + 1)(1 + -4x) Combine like terms: -4x + 15x = 11x (-20 + 11x + 3x2) = (x + 1)(1 + -4x) Reorder the terms: -20 + 11x + 3x2 = (1 + x)(1 + -4x) Multiply (1 + x) * (1 + -4x) -20 + 11x + 3x2 = (1(1 + -4x) + x(1 + -4x)) -20 + 11x + 3x2 = ((1 * 1 + -4x * 1) + x(1 + -4x)) -20 + 11x + 3x2 = ((1 + -4x) + x(1 + -4x)) -20 + 11x + 3x2 = (1 + -4x + (1 * x + -4x * x)) -20 + 11x + 3x2 = (1 + -4x + (1x + -4x2)) Combine like terms: -4x + 1x = -3x -20 + 11x + 3x2 = (1 + -3x + -4x2) Solving -20 + 11x + 3x2 = 1 + -3x + -4x2 Solving for variable 'x'. Reorder the terms: -20 + -1 + 11x + 3x + 3x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2 Combine like terms: -20 + -1 = -21 -21 + 11x + 3x + 3x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2 Combine like terms: 11x + 3x = 14x -21 + 14x + 3x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2 Combine like terms: 3x2 + 4x2 = 7x2 -21 + 14x + 7x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2 Reorder the terms: -21 + 14x + 7x2 = 1 + -1 + -3x + 3x + -4x2 + 4x2 Combine like terms: 1 + -1 = 0 -21 + 14x + 7x2 = 0 + -3x + 3x + -4x2 + 4x2 -21 + 14x + 7x2 = -3x + 3x + -4x2 + 4x2 Combine like terms: -3x + 3x = 0 -21 + 14x + 7x2 = 0 + -4x2 + 4x2 -21 + 14x + 7x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -21 + 14x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-3 + 2x + x2) = 0 Factor a trinomial. 7((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
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 = -3Subproblem 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 = {-3, 1}
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