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Simplifying (9 + -1x)(3)[3 + -1x] = 0 Reorder the terms for easier multiplication: 3(9 + -1x)[3 + -1x] = 0 Multiply (9 + -1x) * [3 + -1x] 3(9[3 + -1x] + -1x * [3 + -1x]) = 0 3([3 * 9 + -1x * 9] + -1x * [3 + -1x]) = 0 3([27 + -9x] + -1x * [3 + -1x]) = 0 3(27 + -9x + [3 * -1x + -1x * -1x]) = 0 3(27 + -9x + [-3x + 1x2]) = 0 Combine like terms: -9x + -3x = -12x 3(27 + -12x + 1x2) = 0 (27 * 3 + -12x * 3 + 1x2 * 3) = 0 (81 + -36x + 3x2) = 0 Solving 81 + -36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -12x + x2) = 0 Factor a trinomial. 3((3 + -1x)(9 + -1x)) = 0 Ignore the factor 3.Subproblem 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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