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Simplifying 6x(x + 9) = (2x + 8)(x + 9) Reorder the terms: 6x(9 + x) = (2x + 8)(x + 9) (9 * 6x + x * 6x) = (2x + 8)(x + 9) (54x + 6x2) = (2x + 8)(x + 9) Reorder the terms: 54x + 6x2 = (8 + 2x)(x + 9) Reorder the terms: 54x + 6x2 = (8 + 2x)(9 + x) Multiply (8 + 2x) * (9 + x) 54x + 6x2 = (8(9 + x) + 2x * (9 + x)) 54x + 6x2 = ((9 * 8 + x * 8) + 2x * (9 + x)) 54x + 6x2 = ((72 + 8x) + 2x * (9 + x)) 54x + 6x2 = (72 + 8x + (9 * 2x + x * 2x)) 54x + 6x2 = (72 + 8x + (18x + 2x2)) Combine like terms: 8x + 18x = 26x 54x + 6x2 = (72 + 26x + 2x2) Solving 54x + 6x2 = 72 + 26x + 2x2 Solving for variable 'x'. Reorder the terms: -72 + 54x + -26x + 6x2 + -2x2 = 72 + 26x + 2x2 + -72 + -26x + -2x2 Combine like terms: 54x + -26x = 28x -72 + 28x + 6x2 + -2x2 = 72 + 26x + 2x2 + -72 + -26x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 -72 + 28x + 4x2 = 72 + 26x + 2x2 + -72 + -26x + -2x2 Reorder the terms: -72 + 28x + 4x2 = 72 + -72 + 26x + -26x + 2x2 + -2x2 Combine like terms: 72 + -72 = 0 -72 + 28x + 4x2 = 0 + 26x + -26x + 2x2 + -2x2 -72 + 28x + 4x2 = 26x + -26x + 2x2 + -2x2 Combine like terms: 26x + -26x = 0 -72 + 28x + 4x2 = 0 + 2x2 + -2x2 -72 + 28x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -72 + 28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + 7x + x2) = 0 Factor a trinomial. 4((-9 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-9, 2}
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