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Simplifying 0 = (2x)(3x + 1) Remove parenthesis around (2x) 0 = 2x(3x + 1) Reorder the terms: 0 = 2x(1 + 3x) 0 = (1 * 2x + 3x * 2x) 0 = (2x + 6x2) Solving 0 = 2x + 6x2 Solving for variable 'x'. Remove the zero: -2x + -6x2 = 2x + 6x2 + -2x + -6x2 Reorder the terms: -2x + -6x2 = 2x + -2x + 6x2 + -6x2 Combine like terms: 2x + -2x = 0 -2x + -6x2 = 0 + 6x2 + -6x2 -2x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(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 '(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, -0.3333333333}
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