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Simplifying (x + -3)(x + -4) = 42 Reorder the terms: (-3 + x)(x + -4) = 42 Reorder the terms: (-3 + x)(-4 + x) = 42 Multiply (-3 + x) * (-4 + x) (-3(-4 + x) + x(-4 + x)) = 42 ((-4 * -3 + x * -3) + x(-4 + x)) = 42 ((12 + -3x) + x(-4 + x)) = 42 (12 + -3x + (-4 * x + x * x)) = 42 (12 + -3x + (-4x + x2)) = 42 Combine like terms: -3x + -4x = -7x (12 + -7x + x2) = 42 Solving 12 + -7x + x2 = 42 Solving for variable 'x'. Reorder the terms: 12 + -42 + -7x + x2 = 42 + -42 Combine like terms: 12 + -42 = -30 -30 + -7x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -30 + -7x + x2 = 0 Factor a trinomial. (-3 + -1x)(10 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-3, 10}
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