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Simplifying (7x + 1)(5x + 12) = 0 Reorder the terms: (1 + 7x)(5x + 12) = 0 Reorder the terms: (1 + 7x)(12 + 5x) = 0 Multiply (1 + 7x) * (12 + 5x) (1(12 + 5x) + 7x * (12 + 5x)) = 0 ((12 * 1 + 5x * 1) + 7x * (12 + 5x)) = 0 ((12 + 5x) + 7x * (12 + 5x)) = 0 (12 + 5x + (12 * 7x + 5x * 7x)) = 0 (12 + 5x + (84x + 35x2)) = 0 Combine like terms: 5x + 84x = 89x (12 + 89x + 35x2) = 0 Solving 12 + 89x + 35x2 = 0 Solving for variable 'x'. Factor a trinomial. (12 + 5x)(1 + 7x) = 0Subproblem 1
Set the factor '(12 + 5x)' equal to zero and attempt to solve: Simplifying 12 + 5x = 0 Solving 12 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5x = 0 + -12 5x = 0 + -12 Combine like terms: 0 + -12 = -12 5x = -12 Divide each side by '5'. x = -2.4 Simplifying x = -2.4Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve: Simplifying 1 + 7x = 0 Solving 1 + 7x = 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 + 7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x = 0 + -1 7x = 0 + -1 Combine like terms: 0 + -1 = -1 7x = -1 Divide each side by '7'. x = -0.1428571429 Simplifying x = -0.1428571429Solution
x = {-2.4, -0.1428571429}
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