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Simplifying (x + 4)(x + -6) + 21 = 0 Reorder the terms: (4 + x)(x + -6) + 21 = 0 Reorder the terms: (4 + x)(-6 + x) + 21 = 0 Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) + 21 = 0 ((-6 * 4 + x * 4) + x(-6 + x)) + 21 = 0 ((-24 + 4x) + x(-6 + x)) + 21 = 0 (-24 + 4x + (-6 * x + x * x)) + 21 = 0 (-24 + 4x + (-6x + x2)) + 21 = 0 Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) + 21 = 0 Reorder the terms: -24 + 21 + -2x + x2 = 0 Combine like terms: -24 + 21 = -3 -3 + -2x + x2 = 0 Solving -3 + -2x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
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 = 3Solution
x = {-1, 3}
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