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Simplifying 300x + -90(300 + -1x) = 2x(300 + -1x) 300x + (300 * -90 + -1x * -90) = 2x(300 + -1x) 300x + (-27000 + 90x) = 2x(300 + -1x) Reorder the terms: -27000 + 300x + 90x = 2x(300 + -1x) Combine like terms: 300x + 90x = 390x -27000 + 390x = 2x(300 + -1x) -27000 + 390x = (300 * 2x + -1x * 2x) -27000 + 390x = (600x + -2x2) Solving -27000 + 390x = 600x + -2x2 Solving for variable 'x'. Combine like terms: 390x + -600x = -210x -27000 + -210x + 2x2 = 600x + -2x2 + -600x + 2x2 Reorder the terms: -27000 + -210x + 2x2 = 600x + -600x + -2x2 + 2x2 Combine like terms: 600x + -600x = 0 -27000 + -210x + 2x2 = 0 + -2x2 + 2x2 -27000 + -210x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -27000 + -210x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13500 + -105x + x2) = 0 Factor a trinomial. 2((-75 + -1x)(180 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + -1x)' equal to zero and attempt to solve: Simplifying -75 + -1x = 0 Solving -75 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + -1x = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -1x = 0 + 75 -1x = 0 + 75 Combine like terms: 0 + 75 = 75 -1x = 75 Divide each side by '-1'. x = -75 Simplifying x = -75Subproblem 2
Set the factor '(180 + -1x)' equal to zero and attempt to solve: Simplifying 180 + -1x = 0 Solving 180 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + -1x = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -1x = 0 + -180 -1x = 0 + -180 Combine like terms: 0 + -180 = -180 -1x = -180 Divide each side by '-1'. x = 180 Simplifying x = 180Solution
x = {-75, 180}
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