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Simplifying 6x(x + 12x) = 6x2 + 72x Combine like terms: x + 12x = 13x 6x(13x) = 6x2 + 72x Remove parenthesis around (13x) 6x * 13x = 6x2 + 72x Reorder the terms for easier multiplication: 6 * 13x * x = 6x2 + 72x Multiply 6 * 13 78x * x = 6x2 + 72x Multiply x * x 78x2 = 6x2 + 72x Reorder the terms: 78x2 = 72x + 6x2 Solving 78x2 = 72x + 6x2 Solving for variable 'x'. Reorder the terms: -72x + 78x2 + -6x2 = 72x + 6x2 + -72x + -6x2 Combine like terms: 78x2 + -6x2 = 72x2 -72x + 72x2 = 72x + 6x2 + -72x + -6x2 Reorder the terms: -72x + 72x2 = 72x + -72x + 6x2 + -6x2 Combine like terms: 72x + -72x = 0 -72x + 72x2 = 0 + 6x2 + -6x2 -72x + 72x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -72x + 72x2 = 0 Factor out the Greatest Common Factor (GCF), '72x'. 72x(-1 + x) = 0 Ignore the factor 72.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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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