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Simplifying (3x + 4)(x + -5) = (2x + -1)(x + -4) Reorder the terms: (4 + 3x)(x + -5) = (2x + -1)(x + -4) Reorder the terms: (4 + 3x)(-5 + x) = (2x + -1)(x + -4) Multiply (4 + 3x) * (-5 + x) (4(-5 + x) + 3x * (-5 + x)) = (2x + -1)(x + -4) ((-5 * 4 + x * 4) + 3x * (-5 + x)) = (2x + -1)(x + -4) ((-20 + 4x) + 3x * (-5 + x)) = (2x + -1)(x + -4) (-20 + 4x + (-5 * 3x + x * 3x)) = (2x + -1)(x + -4) (-20 + 4x + (-15x + 3x2)) = (2x + -1)(x + -4) Combine like terms: 4x + -15x = -11x (-20 + -11x + 3x2) = (2x + -1)(x + -4) Reorder the terms: -20 + -11x + 3x2 = (-1 + 2x)(x + -4) Reorder the terms: -20 + -11x + 3x2 = (-1 + 2x)(-4 + x) Multiply (-1 + 2x) * (-4 + x) -20 + -11x + 3x2 = (-1(-4 + x) + 2x * (-4 + x)) -20 + -11x + 3x2 = ((-4 * -1 + x * -1) + 2x * (-4 + x)) -20 + -11x + 3x2 = ((4 + -1x) + 2x * (-4 + x)) -20 + -11x + 3x2 = (4 + -1x + (-4 * 2x + x * 2x)) -20 + -11x + 3x2 = (4 + -1x + (-8x + 2x2)) Combine like terms: -1x + -8x = -9x -20 + -11x + 3x2 = (4 + -9x + 2x2) Solving -20 + -11x + 3x2 = 4 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -20 + -4 + -11x + 9x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: -20 + -4 = -24 -24 + -11x + 9x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: -11x + 9x = -2x -24 + -2x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -24 + -2x + 1x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Reorder the terms: -24 + -2x + 1x2 = 4 + -4 + -9x + 9x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 -24 + -2x + 1x2 = 0 + -9x + 9x + 2x2 + -2x2 -24 + -2x + 1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -24 + -2x + 1x2 = 0 + 2x2 + -2x2 -24 + -2x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + -2x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-4, 6}
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