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Simplifying 0 = (6x + 5)(5x + 5) Reorder the terms: 0 = (5 + 6x)(5x + 5) Reorder the terms: 0 = (5 + 6x)(5 + 5x) Multiply (5 + 6x) * (5 + 5x) 0 = (5(5 + 5x) + 6x * (5 + 5x)) 0 = ((5 * 5 + 5x * 5) + 6x * (5 + 5x)) 0 = ((25 + 25x) + 6x * (5 + 5x)) 0 = (25 + 25x + (5 * 6x + 5x * 6x)) 0 = (25 + 25x + (30x + 30x2)) Combine like terms: 25x + 30x = 55x 0 = (25 + 55x + 30x2) Solving 0 = 25 + 55x + 30x2 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + -55x + -30x2 = 25 + 55x + 30x2 + -25 + -55x + -30x2 Reorder the terms: -25 + -55x + -30x2 = 25 + -25 + 55x + -55x + 30x2 + -30x2 Combine like terms: 25 + -25 = 0 -25 + -55x + -30x2 = 0 + 55x + -55x + 30x2 + -30x2 -25 + -55x + -30x2 = 55x + -55x + 30x2 + -30x2 Combine like terms: 55x + -55x = 0 -25 + -55x + -30x2 = 0 + 30x2 + -30x2 -25 + -55x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -25 + -55x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(5 + 11x + 6x2) = 0 Factor a trinomial. -5((1 + x)(5 + 6x)) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {-1, -0.8333333333}
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