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Simplifying (6x + 8)(3x + 38) = 0 Reorder the terms: (8 + 6x)(3x + 38) = 0 Reorder the terms: (8 + 6x)(38 + 3x) = 0 Multiply (8 + 6x) * (38 + 3x) (8(38 + 3x) + 6x * (38 + 3x)) = 0 ((38 * 8 + 3x * 8) + 6x * (38 + 3x)) = 0 ((304 + 24x) + 6x * (38 + 3x)) = 0 (304 + 24x + (38 * 6x + 3x * 6x)) = 0 (304 + 24x + (228x + 18x2)) = 0 Combine like terms: 24x + 228x = 252x (304 + 252x + 18x2) = 0 Solving 304 + 252x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(152 + 126x + 9x2) = 0 Factor a trinomial. 2((38 + 3x)(4 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(38 + 3x)' equal to zero and attempt to solve: Simplifying 38 + 3x = 0 Solving 38 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + 3x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 3x = 0 + -38 3x = 0 + -38 Combine like terms: 0 + -38 = -38 3x = -38 Divide each side by '3'. x = -12.66666667 Simplifying x = -12.66666667Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-12.66666667, -1.333333333}
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