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Simplifying 378 = (15 + x)(12 + x) Multiply (15 + x) * (12 + x) 378 = (15(12 + x) + x(12 + x)) 378 = ((12 * 15 + x * 15) + x(12 + x)) 378 = ((180 + 15x) + x(12 + x)) 378 = (180 + 15x + (12 * x + x * x)) 378 = (180 + 15x + (12x + x2)) Combine like terms: 15x + 12x = 27x 378 = (180 + 27x + x2) Solving 378 = 180 + 27x + x2 Solving for variable 'x'. Combine like terms: 378 + -180 = 198 198 + -27x + -1x2 = 180 + 27x + x2 + -180 + -27x + -1x2 Reorder the terms: 198 + -27x + -1x2 = 180 + -180 + 27x + -27x + x2 + -1x2 Combine like terms: 180 + -180 = 0 198 + -27x + -1x2 = 0 + 27x + -27x + x2 + -1x2 198 + -27x + -1x2 = 27x + -27x + x2 + -1x2 Combine like terms: 27x + -27x = 0 198 + -27x + -1x2 = 0 + x2 + -1x2 198 + -27x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 198 + -27x + -1x2 = 0 Factor a trinomial. (6 + -1x)(33 + x) = 0Subproblem 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 '(33 + x)' equal to zero and attempt to solve: Simplifying 33 + x = 0 Solving 33 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + x = 0 + -33 x = 0 + -33 Combine like terms: 0 + -33 = -33 x = -33 Simplifying x = -33Solution
x = {6, -33}
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