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Simplifying (1 + 3x)(x + 5) = 0 Reorder the terms: (1 + 3x)(5 + x) = 0 Multiply (1 + 3x) * (5 + x) (1(5 + x) + 3x * (5 + x)) = 0 ((5 * 1 + x * 1) + 3x * (5 + x)) = 0 ((5 + 1x) + 3x * (5 + x)) = 0 (5 + 1x + (5 * 3x + x * 3x)) = 0 (5 + 1x + (15x + 3x2)) = 0 Combine like terms: 1x + 15x = 16x (5 + 16x + 3x2) = 0 Solving 5 + 16x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + x)(1 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-5, -0.3333333333}
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