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Simplifying (x + 3)(x + -7) = -9 Reorder the terms: (3 + x)(x + -7) = -9 Reorder the terms: (3 + x)(-7 + x) = -9 Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) = -9 ((-7 * 3 + x * 3) + x(-7 + x)) = -9 ((-21 + 3x) + x(-7 + x)) = -9 (-21 + 3x + (-7 * x + x * x)) = -9 (-21 + 3x + (-7x + x2)) = -9 Combine like terms: 3x + -7x = -4x (-21 + -4x + x2) = -9 Solving -21 + -4x + x2 = -9 Solving for variable 'x'. Reorder the terms: -21 + 9 + -4x + x2 = -9 + 9 Combine like terms: -21 + 9 = -12 -12 + -4x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -12 + -4x + x2 = 0 Factor a trinomial. (-2 + -1x)(6 + -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 '(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 = {-2, 6}
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