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Simplifying (x + -3)(x + -3) = 6(x + -3) Reorder the terms: (-3 + x)(x + -3) = 6(x + -3) Reorder the terms: (-3 + x)(-3 + x) = 6(x + -3) Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) = 6(x + -3) ((-3 * -3 + x * -3) + x(-3 + x)) = 6(x + -3) ((9 + -3x) + x(-3 + x)) = 6(x + -3) (9 + -3x + (-3 * x + x * x)) = 6(x + -3) (9 + -3x + (-3x + x2)) = 6(x + -3) Combine like terms: -3x + -3x = -6x (9 + -6x + x2) = 6(x + -3) Reorder the terms: 9 + -6x + x2 = 6(-3 + x) 9 + -6x + x2 = (-3 * 6 + x * 6) 9 + -6x + x2 = (-18 + 6x) Solving 9 + -6x + x2 = -18 + 6x Solving for variable 'x'. Reorder the terms: 9 + 18 + -6x + -6x + x2 = -18 + 6x + 18 + -6x Combine like terms: 9 + 18 = 27 27 + -6x + -6x + x2 = -18 + 6x + 18 + -6x Combine like terms: -6x + -6x = -12x 27 + -12x + x2 = -18 + 6x + 18 + -6x Reorder the terms: 27 + -12x + x2 = -18 + 18 + 6x + -6x Combine like terms: -18 + 18 = 0 27 + -12x + x2 = 0 + 6x + -6x 27 + -12x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 27 + -12x + x2 = 0 Factor a trinomial. (3 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {3, 9}
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