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Simplifying (5x + 1)(x + 3) = 3(x + -1) Reorder the terms: (1 + 5x)(x + 3) = 3(x + -1) Reorder the terms: (1 + 5x)(3 + x) = 3(x + -1) Multiply (1 + 5x) * (3 + x) (1(3 + x) + 5x * (3 + x)) = 3(x + -1) ((3 * 1 + x * 1) + 5x * (3 + x)) = 3(x + -1) ((3 + 1x) + 5x * (3 + x)) = 3(x + -1) (3 + 1x + (3 * 5x + x * 5x)) = 3(x + -1) (3 + 1x + (15x + 5x2)) = 3(x + -1) Combine like terms: 1x + 15x = 16x (3 + 16x + 5x2) = 3(x + -1) Reorder the terms: 3 + 16x + 5x2 = 3(-1 + x) 3 + 16x + 5x2 = (-1 * 3 + x * 3) 3 + 16x + 5x2 = (-3 + 3x) Solving 3 + 16x + 5x2 = -3 + 3x Solving for variable 'x'. Reorder the terms: 3 + 3 + 16x + -3x + 5x2 = -3 + 3x + 3 + -3x Combine like terms: 3 + 3 = 6 6 + 16x + -3x + 5x2 = -3 + 3x + 3 + -3x Combine like terms: 16x + -3x = 13x 6 + 13x + 5x2 = -3 + 3x + 3 + -3x Reorder the terms: 6 + 13x + 5x2 = -3 + 3 + 3x + -3x Combine like terms: -3 + 3 = 0 6 + 13x + 5x2 = 0 + 3x + -3x 6 + 13x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 6 + 13x + 5x2 = 0 Factor a trinomial. (2 + x)(3 + 5x) = 0Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = {-2, -0.6}
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