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Simplifying (x + -4)(x + 3) = 8 Reorder the terms: (-4 + x)(x + 3) = 8 Reorder the terms: (-4 + x)(3 + x) = 8 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) = 8 ((3 * -4 + x * -4) + x(3 + x)) = 8 ((-12 + -4x) + x(3 + x)) = 8 (-12 + -4x + (3 * x + x * x)) = 8 (-12 + -4x + (3x + x2)) = 8 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) = 8 Solving -12 + -1x + x2 = 8 Solving for variable 'x'. Reorder the terms: -12 + -8 + -1x + x2 = 8 + -8 Combine like terms: -12 + -8 = -20 -20 + -1x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -20 + -1x + x2 = 0 Factor a trinomial. (-4 + -1x)(5 + -1x) = 0Subproblem 1
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 = -4Subproblem 2
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 = 5Solution
x = {-4, 5}
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