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Simplifying 2x(x + 6) + -3x(2x + 7) = 0 Reorder the terms: 2x(6 + x) + -3x(2x + 7) = 0 (6 * 2x + x * 2x) + -3x(2x + 7) = 0 (12x + 2x2) + -3x(2x + 7) = 0 Reorder the terms: 12x + 2x2 + -3x(7 + 2x) = 0 12x + 2x2 + (7 * -3x + 2x * -3x) = 0 12x + 2x2 + (-21x + -6x2) = 0 Reorder the terms: 12x + -21x + 2x2 + -6x2 = 0 Combine like terms: 12x + -21x = -9x -9x + 2x2 + -6x2 = 0 Combine like terms: 2x2 + -6x2 = -4x2 -9x + -4x2 = 0 Solving -9x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(9 + 4x) = 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 '(9 + 4x)' equal to zero and attempt to solve: Simplifying 9 + 4x = 0 Solving 9 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x = 0 + -9 4x = 0 + -9 Combine like terms: 0 + -9 = -9 4x = -9 Divide each side by '4'. x = -2.25 Simplifying x = -2.25Solution
x = {0, -2.25}
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