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Simplifying (x + -7)(x + -5) = 3 Reorder the terms: (-7 + x)(x + -5) = 3 Reorder the terms: (-7 + x)(-5 + x) = 3 Multiply (-7 + x) * (-5 + x) (-7(-5 + x) + x(-5 + x)) = 3 ((-5 * -7 + x * -7) + x(-5 + x)) = 3 ((35 + -7x) + x(-5 + x)) = 3 (35 + -7x + (-5 * x + x * x)) = 3 (35 + -7x + (-5x + x2)) = 3 Combine like terms: -7x + -5x = -12x (35 + -12x + x2) = 3 Solving 35 + -12x + x2 = 3 Solving for variable 'x'. Reorder the terms: 35 + -3 + -12x + x2 = 3 + -3 Combine like terms: 35 + -3 = 32 32 + -12x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 32 + -12x + x2 = 0 Factor a trinomial. (4 + -1x)(8 + -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 '(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 = 8Solution
x = {4, 8}
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