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Simplifying (x + -4)(x + 1) = 24 Reorder the terms: (-4 + x)(x + 1) = 24 Reorder the terms: (-4 + x)(1 + x) = 24 Multiply (-4 + x) * (1 + x) (-4(1 + x) + x(1 + x)) = 24 ((1 * -4 + x * -4) + x(1 + x)) = 24 ((-4 + -4x) + x(1 + x)) = 24 (-4 + -4x + (1 * x + x * x)) = 24 (-4 + -4x + (1x + x2)) = 24 Combine like terms: -4x + 1x = -3x (-4 + -3x + x2) = 24 Solving -4 + -3x + x2 = 24 Solving for variable 'x'. Reorder the terms: -4 + -24 + -3x + x2 = 24 + -24 Combine like terms: -4 + -24 = -28 -28 + -3x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -28 + -3x + x2 = 0 Factor a trinomial. (-4 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-4, 7}
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