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Simplifying (x + 4)(x + -5) + -10 = 0 Reorder the terms: (4 + x)(x + -5) + -10 = 0 Reorder the terms: (4 + x)(-5 + x) + -10 = 0 Multiply (4 + x) * (-5 + x) (4(-5 + x) + x(-5 + x)) + -10 = 0 ((-5 * 4 + x * 4) + x(-5 + x)) + -10 = 0 ((-20 + 4x) + x(-5 + x)) + -10 = 0 (-20 + 4x + (-5 * x + x * x)) + -10 = 0 (-20 + 4x + (-5x + x2)) + -10 = 0 Combine like terms: 4x + -5x = -1x (-20 + -1x + x2) + -10 = 0 Reorder the terms: -20 + -10 + -1x + x2 = 0 Combine like terms: -20 + -10 = -30 -30 + -1x + x2 = 0 Solving -30 + -1x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -1x)(6 + -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 '(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 = {-5, 6}
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