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Simplifying 2x(3x + 1)(x + 6) = 0 Reorder the terms: 2x(1 + 3x)(x + 6) = 0 Reorder the terms: 2x(1 + 3x)(6 + x) = 0 Multiply (1 + 3x) * (6 + x) 2x(1(6 + x) + 3x * (6 + x)) = 0 2x((6 * 1 + x * 1) + 3x * (6 + x)) = 0 2x((6 + 1x) + 3x * (6 + x)) = 0 2x(6 + 1x + (6 * 3x + x * 3x)) = 0 2x(6 + 1x + (18x + 3x2)) = 0 Combine like terms: 1x + 18x = 19x 2x(6 + 19x + 3x2) = 0 (6 * 2x + 19x * 2x + 3x2 * 2x) = 0 (12x + 38x2 + 6x3) = 0 Solving 12x + 38x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + 19x + 3x2) = 0 Factor a trinomial. 2x((6 + x)(1 + 3x)) = 0 Ignore the factor 2.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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0, -6, -0.3333333333}
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