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