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Simplifying (4x + 5)(x + -1) = 20x Reorder the terms: (5 + 4x)(x + -1) = 20x Reorder the terms: (5 + 4x)(-1 + x) = 20x Multiply (5 + 4x) * (-1 + x) (5(-1 + x) + 4x * (-1 + x)) = 20x ((-1 * 5 + x * 5) + 4x * (-1 + x)) = 20x ((-5 + 5x) + 4x * (-1 + x)) = 20x (-5 + 5x + (-1 * 4x + x * 4x)) = 20x (-5 + 5x + (-4x + 4x2)) = 20x Combine like terms: 5x + -4x = 1x (-5 + 1x + 4x2) = 20x Solving -5 + 1x + 4x2 = 20x Solving for variable 'x'. Reorder the terms: -5 + 1x + -20x + 4x2 = 20x + -20x Combine like terms: 1x + -20x = -19x -5 + -19x + 4x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -5 + -19x + 4x2 = 0 Factor a trinomial. (-1 + -4x)(5 + -1x) = 0Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
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 = 5Solution
x = {-0.25, 5}
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