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Simplifying (x + 375)(x + 240) = 130500 Reorder the terms: (375 + x)(x + 240) = 130500 Reorder the terms: (375 + x)(240 + x) = 130500 Multiply (375 + x) * (240 + x) (375(240 + x) + x(240 + x)) = 130500 ((240 * 375 + x * 375) + x(240 + x)) = 130500 ((90000 + 375x) + x(240 + x)) = 130500 (90000 + 375x + (240 * x + x * x)) = 130500 (90000 + 375x + (240x + x2)) = 130500 Combine like terms: 375x + 240x = 615x (90000 + 615x + x2) = 130500 Solving 90000 + 615x + x2 = 130500 Solving for variable 'x'. Reorder the terms: 90000 + -130500 + 615x + x2 = 130500 + -130500 Combine like terms: 90000 + -130500 = -40500 -40500 + 615x + x2 = 130500 + -130500 Combine like terms: 130500 + -130500 = 0 -40500 + 615x + x2 = 0 Factor a trinomial. (-675 + -1x)(60 + -1x) = 0Subproblem 1
Set the factor '(-675 + -1x)' equal to zero and attempt to solve: Simplifying -675 + -1x = 0 Solving -675 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '675' to each side of the equation. -675 + 675 + -1x = 0 + 675 Combine like terms: -675 + 675 = 0 0 + -1x = 0 + 675 -1x = 0 + 675 Combine like terms: 0 + 675 = 675 -1x = 675 Divide each side by '-1'. x = -675 Simplifying x = -675Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {-675, 60}
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