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Simplifying (18 + x)(15 + x) = 378 Multiply (18 + x) * (15 + x) (18(15 + x) + x(15 + x)) = 378 ((15 * 18 + x * 18) + x(15 + x)) = 378 ((270 + 18x) + x(15 + x)) = 378 (270 + 18x + (15 * x + x * x)) = 378 (270 + 18x + (15x + x2)) = 378 Combine like terms: 18x + 15x = 33x (270 + 33x + x2) = 378 Solving 270 + 33x + x2 = 378 Solving for variable 'x'. Reorder the terms: 270 + -378 + 33x + x2 = 378 + -378 Combine like terms: 270 + -378 = -108 -108 + 33x + x2 = 378 + -378 Combine like terms: 378 + -378 = 0 -108 + 33x + x2 = 0 Factor a trinomial. (-36 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-36 + -1x)' equal to zero and attempt to solve: Simplifying -36 + -1x = 0 Solving -36 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + -1x = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1x = 0 + 36 -1x = 0 + 36 Combine like terms: 0 + 36 = 36 -1x = 36 Divide each side by '-1'. x = -36 Simplifying x = -36Subproblem 2
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 = 3Solution
x = {-36, 3}
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