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Simplifying (4x + 13)(6x + 2) = 0 Reorder the terms: (13 + 4x)(6x + 2) = 0 Reorder the terms: (13 + 4x)(2 + 6x) = 0 Multiply (13 + 4x) * (2 + 6x) (13(2 + 6x) + 4x * (2 + 6x)) = 0 ((2 * 13 + 6x * 13) + 4x * (2 + 6x)) = 0 ((26 + 78x) + 4x * (2 + 6x)) = 0 (26 + 78x + (2 * 4x + 6x * 4x)) = 0 (26 + 78x + (8x + 24x2)) = 0 Combine like terms: 78x + 8x = 86x (26 + 86x + 24x2) = 0 Solving 26 + 86x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 43x + 12x2) = 0 Factor a trinomial. 2((13 + 4x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 4x)' equal to zero and attempt to solve: Simplifying 13 + 4x = 0 Solving 13 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 4x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 4x = 0 + -13 4x = 0 + -13 Combine like terms: 0 + -13 = -13 4x = -13 Divide each side by '4'. x = -3.25 Simplifying x = -3.25Subproblem 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 = {-3.25, -0.3333333333}
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