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Simplifying 42x + x = 2x(8 + x) Combine like terms: 42x + x = 43x 43x = 2x(8 + x) 43x = (8 * 2x + x * 2x) 43x = (16x + 2x2) Solving 43x = 16x + 2x2 Solving for variable 'x'. Combine like terms: 43x + -16x = 27x 27x + -2x2 = 16x + 2x2 + -16x + -2x2 Reorder the terms: 27x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 27x + -2x2 = 0 + 2x2 + -2x2 27x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 27x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(27 + -2x) = 0Subproblem 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 '(27 + -2x)' equal to zero and attempt to solve: Simplifying 27 + -2x = 0 Solving 27 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -2x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -2x = 0 + -27 -2x = 0 + -27 Combine like terms: 0 + -27 = -27 -2x = -27 Divide each side by '-2'. x = 13.5 Simplifying x = 13.5Solution
x = {0, 13.5}
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