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Simplifying 2x(3x + 2) + -3x(4x + 2) = 0 Reorder the terms: 2x(2 + 3x) + -3x(4x + 2) = 0 (2 * 2x + 3x * 2x) + -3x(4x + 2) = 0 (4x + 6x2) + -3x(4x + 2) = 0 Reorder the terms: 4x + 6x2 + -3x(2 + 4x) = 0 4x + 6x2 + (2 * -3x + 4x * -3x) = 0 4x + 6x2 + (-6x + -12x2) = 0 Reorder the terms: 4x + -6x + 6x2 + -12x2 = 0 Combine like terms: 4x + -6x = -2x -2x + 6x2 + -12x2 = 0 Combine like terms: 6x2 + -12x2 = -6x2 -2x + -6x2 = 0 Solving -2x + -6x2 = 0 Solving for variable 'x'. 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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