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Simplifying (3 + x)(4 + x) = 56 Multiply (3 + x) * (4 + x) (3(4 + x) + x(4 + x)) = 56 ((4 * 3 + x * 3) + x(4 + x)) = 56 ((12 + 3x) + x(4 + x)) = 56 (12 + 3x + (4 * x + x * x)) = 56 (12 + 3x + (4x + x2)) = 56 Combine like terms: 3x + 4x = 7x (12 + 7x + x2) = 56 Solving 12 + 7x + x2 = 56 Solving for variable 'x'. Reorder the terms: 12 + -56 + 7x + x2 = 56 + -56 Combine like terms: 12 + -56 = -44 -44 + 7x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -44 + 7x + x2 = 0 Factor a trinomial. (-11 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-11, 4}
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