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Simplifying (3x + 1)(x2 + 2x) = 0 Reorder the terms: (1 + 3x)(x2 + 2x) = 0 Reorder the terms: (1 + 3x)(2x + x2) = 0 Multiply (1 + 3x) * (2x + x2) (1(2x + x2) + 3x * (2x + x2)) = 0 ((2x * 1 + x2 * 1) + 3x * (2x + x2)) = 0 ((2x + 1x2) + 3x * (2x + x2)) = 0 (2x + 1x2 + (2x * 3x + x2 * 3x)) = 0 (2x + 1x2 + (6x2 + 3x3)) = 0 Combine like terms: 1x2 + 6x2 = 7x2 (2x + 7x2 + 3x3) = 0 Solving 2x + 7x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 7x + 3x2) = 0 Factor a trinomial. x((2 + x)(1 + 3x)) = 0Subproblem 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 '(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 = -2Subproblem 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, -2, -0.3333333333}
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