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Simplifying (16 + x)(12 + x) = 396 Multiply (16 + x) * (12 + x) (16(12 + x) + x(12 + x)) = 396 ((12 * 16 + x * 16) + x(12 + x)) = 396 ((192 + 16x) + x(12 + x)) = 396 (192 + 16x + (12 * x + x * x)) = 396 (192 + 16x + (12x + x2)) = 396 Combine like terms: 16x + 12x = 28x (192 + 28x + x2) = 396 Solving 192 + 28x + x2 = 396 Solving for variable 'x'. Reorder the terms: 192 + -396 + 28x + x2 = 396 + -396 Combine like terms: 192 + -396 = -204 -204 + 28x + x2 = 396 + -396 Combine like terms: 396 + -396 = 0 -204 + 28x + x2 = 0 Factor a trinomial. (-34 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve: Simplifying -34 + -1x = 0 Solving -34 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + -1x = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -1x = 0 + 34 -1x = 0 + 34 Combine like terms: 0 + 34 = 34 -1x = 34 Divide each side by '-1'. x = -34 Simplifying x = -34Subproblem 2
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 = 6Solution
x = {-34, 6}
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