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Simplifying (x + 2)(x + -3) = 2(5x + -17) + 28 Reorder the terms: (2 + x)(x + -3) = 2(5x + -17) + 28 Reorder the terms: (2 + x)(-3 + x) = 2(5x + -17) + 28 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = 2(5x + -17) + 28 ((-3 * 2 + x * 2) + x(-3 + x)) = 2(5x + -17) + 28 ((-6 + 2x) + x(-3 + x)) = 2(5x + -17) + 28 (-6 + 2x + (-3 * x + x * x)) = 2(5x + -17) + 28 (-6 + 2x + (-3x + x2)) = 2(5x + -17) + 28 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = 2(5x + -17) + 28 Reorder the terms: -6 + -1x + x2 = 2(-17 + 5x) + 28 -6 + -1x + x2 = (-17 * 2 + 5x * 2) + 28 -6 + -1x + x2 = (-34 + 10x) + 28 Reorder the terms: -6 + -1x + x2 = -34 + 28 + 10x Combine like terms: -34 + 28 = -6 -6 + -1x + x2 = -6 + 10x Add '6' to each side of the equation. -6 + -1x + 6 + x2 = -6 + 6 + 10x Reorder the terms: -6 + 6 + -1x + x2 = -6 + 6 + 10x Combine like terms: -6 + 6 = 0 0 + -1x + x2 = -6 + 6 + 10x -1x + x2 = -6 + 6 + 10x Combine like terms: -6 + 6 = 0 -1x + x2 = 0 + 10x -1x + x2 = 10x Solving -1x + x2 = 10x Solving for variable 'x'. Reorder the terms: -1x + -10x + x2 = 10x + -10x Combine like terms: -1x + -10x = -11x -11x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -11x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Solution
x = {0, 11}
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