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Simplifying x(5x + -20) + 2(5x + -20) = 5(5x + -20) Reorder the terms: x(-20 + 5x) + 2(5x + -20) = 5(5x + -20) (-20 * x + 5x * x) + 2(5x + -20) = 5(5x + -20) (-20x + 5x2) + 2(5x + -20) = 5(5x + -20) Reorder the terms: -20x + 5x2 + 2(-20 + 5x) = 5(5x + -20) -20x + 5x2 + (-20 * 2 + 5x * 2) = 5(5x + -20) -20x + 5x2 + (-40 + 10x) = 5(5x + -20) Reorder the terms: -40 + -20x + 10x + 5x2 = 5(5x + -20) Combine like terms: -20x + 10x = -10x -40 + -10x + 5x2 = 5(5x + -20) Reorder the terms: -40 + -10x + 5x2 = 5(-20 + 5x) -40 + -10x + 5x2 = (-20 * 5 + 5x * 5) -40 + -10x + 5x2 = (-100 + 25x) Solving -40 + -10x + 5x2 = -100 + 25x Solving for variable 'x'. Reorder the terms: -40 + 100 + -10x + -25x + 5x2 = -100 + 25x + 100 + -25x Combine like terms: -40 + 100 = 60 60 + -10x + -25x + 5x2 = -100 + 25x + 100 + -25x Combine like terms: -10x + -25x = -35x 60 + -35x + 5x2 = -100 + 25x + 100 + -25x Reorder the terms: 60 + -35x + 5x2 = -100 + 100 + 25x + -25x Combine like terms: -100 + 100 = 0 60 + -35x + 5x2 = 0 + 25x + -25x 60 + -35x + 5x2 = 25x + -25x Combine like terms: 25x + -25x = 0 60 + -35x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(12 + -7x + x2) = 0 Factor a trinomial. 5((3 + -1x)(4 + -1x)) = 0 Ignore the factor 5.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 '(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 = 4Solution
x = {3, 4}
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