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Simplifying x2 + -3x + 27 = 6x + 27 Reorder the terms: 27 + -3x + x2 = 6x + 27 Reorder the terms: 27 + -3x + x2 = 27 + 6x Add '-27' to each side of the equation. 27 + -3x + -27 + x2 = 27 + -27 + 6x Reorder the terms: 27 + -27 + -3x + x2 = 27 + -27 + 6x Combine like terms: 27 + -27 = 0 0 + -3x + x2 = 27 + -27 + 6x -3x + x2 = 27 + -27 + 6x Combine like terms: 27 + -27 = 0 -3x + x2 = 0 + 6x -3x + x2 = 6x Solving -3x + x2 = 6x Solving for variable 'x'. Reorder the terms: -3x + -6x + x2 = 6x + -6x Combine like terms: -3x + -6x = -9x -9x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -9x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + x) = 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 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 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Solution
x = {0, 9}
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