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Simplifying (6 + 4x)(15x + 25) = 0 Reorder the terms: (6 + 4x)(25 + 15x) = 0 Multiply (6 + 4x) * (25 + 15x) (6(25 + 15x) + 4x * (25 + 15x)) = 0 ((25 * 6 + 15x * 6) + 4x * (25 + 15x)) = 0 ((150 + 90x) + 4x * (25 + 15x)) = 0 (150 + 90x + (25 * 4x + 15x * 4x)) = 0 (150 + 90x + (100x + 60x2)) = 0 Combine like terms: 90x + 100x = 190x (150 + 190x + 60x2) = 0 Solving 150 + 190x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(15 + 19x + 6x2) = 0 Factor a trinomial. 10((5 + 3x)(3 + 2x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-1.666666667, -1.5}
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