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Simplifying (15x + 105)(-3x + 51) = 0 Reorder the terms: (105 + 15x)(-3x + 51) = 0 Reorder the terms: (105 + 15x)(51 + -3x) = 0 Multiply (105 + 15x) * (51 + -3x) (105(51 + -3x) + 15x * (51 + -3x)) = 0 ((51 * 105 + -3x * 105) + 15x * (51 + -3x)) = 0 ((5355 + -315x) + 15x * (51 + -3x)) = 0 (5355 + -315x + (51 * 15x + -3x * 15x)) = 0 (5355 + -315x + (765x + -45x2)) = 0 Combine like terms: -315x + 765x = 450x (5355 + 450x + -45x2) = 0 Solving 5355 + 450x + -45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '45'. 45(119 + 10x + -1x2) = 0 Factor a trinomial. 45((17 + -1x)(7 + x)) = 0 Ignore the factor 45.Subproblem 1
Set the factor '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {17, -7}
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