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