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Simplifying (4x + 5)(x + -5) = 12x + 15 Reorder the terms: (5 + 4x)(x + -5) = 12x + 15 Reorder the terms: (5 + 4x)(-5 + x) = 12x + 15 Multiply (5 + 4x) * (-5 + x) (5(-5 + x) + 4x * (-5 + x)) = 12x + 15 ((-5 * 5 + x * 5) + 4x * (-5 + x)) = 12x + 15 ((-25 + 5x) + 4x * (-5 + x)) = 12x + 15 (-25 + 5x + (-5 * 4x + x * 4x)) = 12x + 15 (-25 + 5x + (-20x + 4x2)) = 12x + 15 Combine like terms: 5x + -20x = -15x (-25 + -15x + 4x2) = 12x + 15 Reorder the terms: -25 + -15x + 4x2 = 15 + 12x Solving -25 + -15x + 4x2 = 15 + 12x Solving for variable 'x'. Reorder the terms: -25 + -15 + -15x + -12x + 4x2 = 15 + 12x + -15 + -12x Combine like terms: -25 + -15 = -40 -40 + -15x + -12x + 4x2 = 15 + 12x + -15 + -12x Combine like terms: -15x + -12x = -27x -40 + -27x + 4x2 = 15 + 12x + -15 + -12x Reorder the terms: -40 + -27x + 4x2 = 15 + -15 + 12x + -12x Combine like terms: 15 + -15 = 0 -40 + -27x + 4x2 = 0 + 12x + -12x -40 + -27x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -40 + -27x + 4x2 = 0 Factor a trinomial. (-5 + -4x)(8 + -1x) = 0Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-1.25, 8}
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