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Simplifying (3x + 9)(10x + 30) = 0 Reorder the terms: (9 + 3x)(10x + 30) = 0 Reorder the terms: (9 + 3x)(30 + 10x) = 0 Multiply (9 + 3x) * (30 + 10x) (9(30 + 10x) + 3x * (30 + 10x)) = 0 ((30 * 9 + 10x * 9) + 3x * (30 + 10x)) = 0 ((270 + 90x) + 3x * (30 + 10x)) = 0 (270 + 90x + (30 * 3x + 10x * 3x)) = 0 (270 + 90x + (90x + 30x2)) = 0 Combine like terms: 90x + 90x = 180x (270 + 180x + 30x2) = 0 Solving 270 + 180x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '30'. 30(9 + 6x + x2) = 0 Factor a trinomial. 30((3 + x)(3 + x)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-3, -3}
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