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Simplifying 2x(2x + 6) = 3x(2x + 4x) Reorder the terms: 2x(6 + 2x) = 3x(2x + 4x) (6 * 2x + 2x * 2x) = 3x(2x + 4x) (12x + 4x2) = 3x(2x + 4x) Combine like terms: 2x + 4x = 6x 12x + 4x2 = 3x(6x) Remove parenthesis around (6x) 12x + 4x2 = 3x * 6x Reorder the terms for easier multiplication: 12x + 4x2 = 3 * 6x * x Multiply 3 * 6 12x + 4x2 = 18x * x Multiply x * x 12x + 4x2 = 18x2 Solving 12x + 4x2 = 18x2 Solving for variable 'x'. Combine like terms: 4x2 + -18x2 = -14x2 12x + -14x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 12x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + -7x) = 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 '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571Solution
x = {0, 0.8571428571}
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