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Simplifying 6x(3 + -1x)(x + 2) = 0 Reorder the terms: 6x(3 + -1x)(2 + x) = 0 Multiply (3 + -1x) * (2 + x) 6x(3(2 + x) + -1x * (2 + x)) = 0 6x((2 * 3 + x * 3) + -1x * (2 + x)) = 0 6x((6 + 3x) + -1x * (2 + x)) = 0 6x(6 + 3x + (2 * -1x + x * -1x)) = 0 6x(6 + 3x + (-2x + -1x2)) = 0 Combine like terms: 3x + -2x = 1x 6x(6 + 1x + -1x2) = 0 (6 * 6x + 1x * 6x + -1x2 * 6x) = 0 (36x + 6x2 + -6x3) = 0 Solving 36x + 6x2 + -6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(6 + x + -1x2) = 0 Factor a trinomial. 6x((3 + -1x)(2 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
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 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, 3, -2}
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