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Simplifying (x + 3)(x + -2) + (x + 3) = 0 Reorder the terms: (3 + x)(x + -2) + (x + 3) = 0 Reorder the terms: (3 + x)(-2 + x) + (x + 3) = 0 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) + (x + 3) = 0 ((-2 * 3 + x * 3) + x(-2 + x)) + (x + 3) = 0 ((-6 + 3x) + x(-2 + x)) + (x + 3) = 0 (-6 + 3x + (-2 * x + x * x)) + (x + 3) = 0 (-6 + 3x + (-2x + x2)) + (x + 3) = 0 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) + (x + 3) = 0 Reorder the terms: -6 + 1x + x2 + (3 + x) = 0 Remove parenthesis around (3 + x) -6 + 1x + x2 + 3 + x = 0 Reorder the terms: -6 + 3 + 1x + x + x2 = 0 Combine like terms: -6 + 3 = -3 -3 + 1x + x + x2 = 0 Combine like terms: 1x + x = 2x -3 + 2x + x2 = 0 Solving -3 + 2x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -1x)(1 + -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 '(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 = 1Solution
x = {-3, 1}
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