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Simplifying (x + 2)(x + 4) = 7x + 38 Reorder the terms: (2 + x)(x + 4) = 7x + 38 Reorder the terms: (2 + x)(4 + x) = 7x + 38 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 7x + 38 ((4 * 2 + x * 2) + x(4 + x)) = 7x + 38 ((8 + 2x) + x(4 + x)) = 7x + 38 (8 + 2x + (4 * x + x * x)) = 7x + 38 (8 + 2x + (4x + x2)) = 7x + 38 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 7x + 38 Reorder the terms: 8 + 6x + x2 = 38 + 7x Solving 8 + 6x + x2 = 38 + 7x Solving for variable 'x'. Reorder the terms: 8 + -38 + 6x + -7x + x2 = 38 + 7x + -38 + -7x Combine like terms: 8 + -38 = -30 -30 + 6x + -7x + x2 = 38 + 7x + -38 + -7x Combine like terms: 6x + -7x = -1x -30 + -1x + x2 = 38 + 7x + -38 + -7x Reorder the terms: -30 + -1x + x2 = 38 + -38 + 7x + -7x Combine like terms: 38 + -38 = 0 -30 + -1x + x2 = 0 + 7x + -7x -30 + -1x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -30 + -1x + x2 = 0 Factor a trinomial. (-5 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 6}
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