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Simplifying (3x + 3) * x = 6 Reorder the terms: (3 + 3x) * x = 6 Reorder the terms for easier multiplication: x(3 + 3x) = 6 (3 * x + 3x * x) = 6 (3x + 3x2) = 6 Solving 3x + 3x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 3x + 3x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + x + x2) = 0 Factor a trinomial. 3((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 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 = {-2, 1}
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