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Simplifying 3000(x + 18) = 3000x + 375x(18 + x) Reorder the terms: 3000(18 + x) = 3000x + 375x(18 + x) (18 * 3000 + x * 3000) = 3000x + 375x(18 + x) (54000 + 3000x) = 3000x + 375x(18 + x) 54000 + 3000x = 3000x + (18 * 375x + x * 375x) 54000 + 3000x = 3000x + (6750x + 375x2) Combine like terms: 3000x + 6750x = 9750x 54000 + 3000x = 9750x + 375x2 Solving 54000 + 3000x = 9750x + 375x2 Solving for variable 'x'. Combine like terms: 3000x + -9750x = -6750x 54000 + -6750x + -375x2 = 9750x + 375x2 + -9750x + -375x2 Reorder the terms: 54000 + -6750x + -375x2 = 9750x + -9750x + 375x2 + -375x2 Combine like terms: 9750x + -9750x = 0 54000 + -6750x + -375x2 = 0 + 375x2 + -375x2 54000 + -6750x + -375x2 = 375x2 + -375x2 Combine like terms: 375x2 + -375x2 = 0 54000 + -6750x + -375x2 = 0 Factor out the Greatest Common Factor (GCF), '375'. 375(144 + -18x + -1x2) = 0 Factor a trinomial. 375((6 + -1x)(24 + x)) = 0 Ignore the factor 375.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(24 + x)' equal to zero and attempt to solve: Simplifying 24 + x = 0 Solving 24 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + x = 0 + -24 x = 0 + -24 Combine like terms: 0 + -24 = -24 x = -24 Simplifying x = -24Solution
x = {6, -24}
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