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Simplifying (x + 2)(x + 4) = 323 Reorder the terms: (2 + x)(x + 4) = 323 Reorder the terms: (2 + x)(4 + x) = 323 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 323 ((4 * 2 + x * 2) + x(4 + x)) = 323 ((8 + 2x) + x(4 + x)) = 323 (8 + 2x + (4 * x + x * x)) = 323 (8 + 2x + (4x + x2)) = 323 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 323 Solving 8 + 6x + x2 = 323 Solving for variable 'x'. Reorder the terms: 8 + -323 + 6x + x2 = 323 + -323 Combine like terms: 8 + -323 = -315 -315 + 6x + x2 = 323 + -323 Combine like terms: 323 + -323 = 0 -315 + 6x + x2 = 0 Factor a trinomial. (-21 + -1x)(15 + -1x) = 0Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-21, 15}
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