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Simplifying (x + -3)(x + -4) = 2 Reorder the terms: (-3 + x)(x + -4) = 2 Reorder the terms: (-3 + x)(-4 + x) = 2 Multiply (-3 + x) * (-4 + x) (-3(-4 + x) + x(-4 + x)) = 2 ((-4 * -3 + x * -3) + x(-4 + x)) = 2 ((12 + -3x) + x(-4 + x)) = 2 (12 + -3x + (-4 * x + x * x)) = 2 (12 + -3x + (-4x + x2)) = 2 Combine like terms: -3x + -4x = -7x (12 + -7x + x2) = 2 Solving 12 + -7x + x2 = 2 Solving for variable 'x'. Reorder the terms: 12 + -2 + -7x + x2 = 2 + -2 Combine like terms: 12 + -2 = 10 10 + -7x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 10 + -7x + x2 = 0 Factor a trinomial. (2 + -1x)(5 + -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 '(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 = {2, 5}
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