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Simplifying (x + 1)(x + -5) = 7 Reorder the terms: (1 + x)(x + -5) = 7 Reorder the terms: (1 + x)(-5 + x) = 7 Multiply (1 + x) * (-5 + x) (1(-5 + x) + x(-5 + x)) = 7 ((-5 * 1 + x * 1) + x(-5 + x)) = 7 ((-5 + 1x) + x(-5 + x)) = 7 (-5 + 1x + (-5 * x + x * x)) = 7 (-5 + 1x + (-5x + x2)) = 7 Combine like terms: 1x + -5x = -4x (-5 + -4x + x2) = 7 Solving -5 + -4x + x2 = 7 Solving for variable 'x'. Reorder the terms: -5 + -7 + -4x + x2 = 7 + -7 Combine like terms: -5 + -7 = -12 -12 + -4x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -12 + -4x + x2 = 0 Factor a trinomial. (-2 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 6}
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