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Simplifying (5x + 1)(3 + x) = -2(5x + 1) Reorder the terms: (1 + 5x)(3 + x) = -2(5x + 1) Multiply (1 + 5x) * (3 + x) (1(3 + x) + 5x * (3 + x)) = -2(5x + 1) ((3 * 1 + x * 1) + 5x * (3 + x)) = -2(5x + 1) ((3 + 1x) + 5x * (3 + x)) = -2(5x + 1) (3 + 1x + (3 * 5x + x * 5x)) = -2(5x + 1) (3 + 1x + (15x + 5x2)) = -2(5x + 1) Combine like terms: 1x + 15x = 16x (3 + 16x + 5x2) = -2(5x + 1) Reorder the terms: 3 + 16x + 5x2 = -2(1 + 5x) 3 + 16x + 5x2 = (1 * -2 + 5x * -2) 3 + 16x + 5x2 = (-2 + -10x) Solving 3 + 16x + 5x2 = -2 + -10x Solving for variable 'x'. Reorder the terms: 3 + 2 + 16x + 10x + 5x2 = -2 + -10x + 2 + 10x Combine like terms: 3 + 2 = 5 5 + 16x + 10x + 5x2 = -2 + -10x + 2 + 10x Combine like terms: 16x + 10x = 26x 5 + 26x + 5x2 = -2 + -10x + 2 + 10x Reorder the terms: 5 + 26x + 5x2 = -2 + 2 + -10x + 10x Combine like terms: -2 + 2 = 0 5 + 26x + 5x2 = 0 + -10x + 10x 5 + 26x + 5x2 = -10x + 10x Combine like terms: -10x + 10x = 0 5 + 26x + 5x2 = 0 Factor a trinomial. (5 + x)(1 + 5x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {-5, -0.2}
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