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Simplifying (x + -4)(x + 7) = 4(x + 11) Reorder the terms: (-4 + x)(x + 7) = 4(x + 11) Reorder the terms: (-4 + x)(7 + x) = 4(x + 11) Multiply (-4 + x) * (7 + x) (-4(7 + x) + x(7 + x)) = 4(x + 11) ((7 * -4 + x * -4) + x(7 + x)) = 4(x + 11) ((-28 + -4x) + x(7 + x)) = 4(x + 11) (-28 + -4x + (7 * x + x * x)) = 4(x + 11) (-28 + -4x + (7x + x2)) = 4(x + 11) Combine like terms: -4x + 7x = 3x (-28 + 3x + x2) = 4(x + 11) Reorder the terms: -28 + 3x + x2 = 4(11 + x) -28 + 3x + x2 = (11 * 4 + x * 4) -28 + 3x + x2 = (44 + 4x) Solving -28 + 3x + x2 = 44 + 4x Solving for variable 'x'. Reorder the terms: -28 + -44 + 3x + -4x + x2 = 44 + 4x + -44 + -4x Combine like terms: -28 + -44 = -72 -72 + 3x + -4x + x2 = 44 + 4x + -44 + -4x Combine like terms: 3x + -4x = -1x -72 + -1x + x2 = 44 + 4x + -44 + -4x Reorder the terms: -72 + -1x + x2 = 44 + -44 + 4x + -4x Combine like terms: 44 + -44 = 0 -72 + -1x + x2 = 0 + 4x + -4x -72 + -1x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -72 + -1x + x2 = 0 Factor a trinomial. (-8 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-8, 9}
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