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Simplifying 3(2x2 + 3x) = 4(2x2 + 3x) Reorder the terms: 3(3x + 2x2) = 4(2x2 + 3x) (3x * 3 + 2x2 * 3) = 4(2x2 + 3x) (9x + 6x2) = 4(2x2 + 3x) Reorder the terms: 9x + 6x2 = 4(3x + 2x2) 9x + 6x2 = (3x * 4 + 2x2 * 4) 9x + 6x2 = (12x + 8x2) Solving 9x + 6x2 = 12x + 8x2 Solving for variable 'x'. Reorder the terms: 9x + -12x + 6x2 + -8x2 = 12x + 8x2 + -12x + -8x2 Combine like terms: 9x + -12x = -3x -3x + 6x2 + -8x2 = 12x + 8x2 + -12x + -8x2 Combine like terms: 6x2 + -8x2 = -2x2 -3x + -2x2 = 12x + 8x2 + -12x + -8x2 Reorder the terms: -3x + -2x2 = 12x + -12x + 8x2 + -8x2 Combine like terms: 12x + -12x = 0 -3x + -2x2 = 0 + 8x2 + -8x2 -3x + -2x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(3 + 2x) = 0 Ignore the factor -1.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 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -1.5}
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