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Simplifying x2 + 6x + (3x + 5)(x + 6) = 0 Reorder the terms: x2 + 6x + (5 + 3x)(x + 6) = 0 Reorder the terms: x2 + 6x + (5 + 3x)(6 + x) = 0 Multiply (5 + 3x) * (6 + x) x2 + 6x + (5(6 + x) + 3x * (6 + x)) = 0 x2 + 6x + ((6 * 5 + x * 5) + 3x * (6 + x)) = 0 x2 + 6x + ((30 + 5x) + 3x * (6 + x)) = 0 x2 + 6x + (30 + 5x + (6 * 3x + x * 3x)) = 0 x2 + 6x + (30 + 5x + (18x + 3x2)) = 0 Combine like terms: 5x + 18x = 23x x2 + 6x + (30 + 23x + 3x2) = 0 Reorder the terms: 30 + 6x + 23x + x2 + 3x2 = 0 Combine like terms: 6x + 23x = 29x 30 + 29x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 30 + 29x + 4x2 = 0 Solving 30 + 29x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(5 + 4x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
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 = -1.25Solution
x = {-6, -1.25}
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