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Simplifying (x + 5)(3x + -4) = (x + 1)(x + 5) Reorder the terms: (5 + x)(3x + -4) = (x + 1)(x + 5) Reorder the terms: (5 + x)(-4 + 3x) = (x + 1)(x + 5) Multiply (5 + x) * (-4 + 3x) (5(-4 + 3x) + x(-4 + 3x)) = (x + 1)(x + 5) ((-4 * 5 + 3x * 5) + x(-4 + 3x)) = (x + 1)(x + 5) ((-20 + 15x) + x(-4 + 3x)) = (x + 1)(x + 5) (-20 + 15x + (-4 * x + 3x * x)) = (x + 1)(x + 5) (-20 + 15x + (-4x + 3x2)) = (x + 1)(x + 5) Combine like terms: 15x + -4x = 11x (-20 + 11x + 3x2) = (x + 1)(x + 5) Reorder the terms: -20 + 11x + 3x2 = (1 + x)(x + 5) Reorder the terms: -20 + 11x + 3x2 = (1 + x)(5 + x) Multiply (1 + x) * (5 + x) -20 + 11x + 3x2 = (1(5 + x) + x(5 + x)) -20 + 11x + 3x2 = ((5 * 1 + x * 1) + x(5 + x)) -20 + 11x + 3x2 = ((5 + 1x) + x(5 + x)) -20 + 11x + 3x2 = (5 + 1x + (5 * x + x * x)) -20 + 11x + 3x2 = (5 + 1x + (5x + x2)) Combine like terms: 1x + 5x = 6x -20 + 11x + 3x2 = (5 + 6x + x2) Solving -20 + 11x + 3x2 = 5 + 6x + x2 Solving for variable 'x'. Reorder the terms: -20 + -5 + 11x + -6x + 3x2 + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2 Combine like terms: -20 + -5 = -25 -25 + 11x + -6x + 3x2 + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2 Combine like terms: 11x + -6x = 5x -25 + 5x + 3x2 + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -25 + 5x + 2x2 = 5 + 6x + x2 + -5 + -6x + -1x2 Reorder the terms: -25 + 5x + 2x2 = 5 + -5 + 6x + -6x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -25 + 5x + 2x2 = 0 + 6x + -6x + x2 + -1x2 -25 + 5x + 2x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -25 + 5x + 2x2 = 0 + x2 + -1x2 -25 + 5x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -25 + 5x + 2x2 = 0 Factor a trinomial. (-5 + -1x)(5 + -2x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-5, 2.5}
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