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Simplifying (x + 10)(5x + 3) = (3 + 5x) Reorder the terms: (10 + x)(5x + 3) = (3 + 5x) Reorder the terms: (10 + x)(3 + 5x) = (3 + 5x) Multiply (10 + x) * (3 + 5x) (10(3 + 5x) + x(3 + 5x)) = (3 + 5x) ((3 * 10 + 5x * 10) + x(3 + 5x)) = (3 + 5x) ((30 + 50x) + x(3 + 5x)) = (3 + 5x) (30 + 50x + (3 * x + 5x * x)) = (3 + 5x) (30 + 50x + (3x + 5x2)) = (3 + 5x) Combine like terms: 50x + 3x = 53x (30 + 53x + 5x2) = (3 + 5x) Remove parenthesis around (3 + 5x) 30 + 53x + 5x2 = 3 + 5x Solving 30 + 53x + 5x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: 30 + -3 + 53x + -5x + 5x2 = 3 + 5x + -3 + -5x Combine like terms: 30 + -3 = 27 27 + 53x + -5x + 5x2 = 3 + 5x + -3 + -5x Combine like terms: 53x + -5x = 48x 27 + 48x + 5x2 = 3 + 5x + -3 + -5x Reorder the terms: 27 + 48x + 5x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 27 + 48x + 5x2 = 0 + 5x + -5x 27 + 48x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 27 + 48x + 5x2 = 0 Factor a trinomial. (9 + x)(3 + 5x) = 0Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Solution
x = {-9, -0.6}
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