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Simplifying (3x + 1)(4x + 5) = 0 Reorder the terms: (1 + 3x)(4x + 5) = 0 Reorder the terms: (1 + 3x)(5 + 4x) = 0 Multiply (1 + 3x) * (5 + 4x) (1(5 + 4x) + 3x * (5 + 4x)) = 0 ((5 * 1 + 4x * 1) + 3x * (5 + 4x)) = 0 ((5 + 4x) + 3x * (5 + 4x)) = 0 (5 + 4x + (5 * 3x + 4x * 3x)) = 0 (5 + 4x + (15x + 12x2)) = 0 Combine like terms: 4x + 15x = 19x (5 + 19x + 12x2) = 0 Solving 5 + 19x + 12x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + 4x)(1 + 3x) = 0Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Subproblem 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 = {-1.25, -0.3333333333}
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