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Simplifying (5x + 27)(3x + 17) = 0 Reorder the terms: (27 + 5x)(3x + 17) = 0 Reorder the terms: (27 + 5x)(17 + 3x) = 0 Multiply (27 + 5x) * (17 + 3x) (27(17 + 3x) + 5x * (17 + 3x)) = 0 ((17 * 27 + 3x * 27) + 5x * (17 + 3x)) = 0 ((459 + 81x) + 5x * (17 + 3x)) = 0 (459 + 81x + (17 * 5x + 3x * 5x)) = 0 (459 + 81x + (85x + 15x2)) = 0 Combine like terms: 81x + 85x = 166x (459 + 166x + 15x2) = 0 Solving 459 + 166x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (17 + 3x)(27 + 5x) = 0Subproblem 1
Set the factor '(17 + 3x)' equal to zero and attempt to solve: Simplifying 17 + 3x = 0 Solving 17 + 3x = 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 + 3x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 3x = 0 + -17 3x = 0 + -17 Combine like terms: 0 + -17 = -17 3x = -17 Divide each side by '3'. x = -5.666666667 Simplifying x = -5.666666667Subproblem 2
Set the factor '(27 + 5x)' equal to zero and attempt to solve: Simplifying 27 + 5x = 0 Solving 27 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 5x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 5x = 0 + -27 5x = 0 + -27 Combine like terms: 0 + -27 = -27 5x = -27 Divide each side by '5'. x = -5.4 Simplifying x = -5.4Solution
x = {-5.666666667, -5.4}
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