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Simplifying (5x + 6)(7x + 7) = 0 Reorder the terms: (6 + 5x)(7x + 7) = 0 Reorder the terms: (6 + 5x)(7 + 7x) = 0 Multiply (6 + 5x) * (7 + 7x) (6(7 + 7x) + 5x * (7 + 7x)) = 0 ((7 * 6 + 7x * 6) + 5x * (7 + 7x)) = 0 ((42 + 42x) + 5x * (7 + 7x)) = 0 (42 + 42x + (7 * 5x + 7x * 5x)) = 0 (42 + 42x + (35x + 35x2)) = 0 Combine like terms: 42x + 35x = 77x (42 + 77x + 35x2) = 0 Solving 42 + 77x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(6 + 11x + 5x2) = 0 Factor a trinomial. 7((6 + 5x)(1 + x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 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 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Divide each side by '5'. x = -1.2 Simplifying x = -1.2Subproblem 2
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 = -1Solution
x = {-1.2, -1}
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