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Simplifying 0 = (7x + 5)(2x + -3) Reorder the terms: 0 = (5 + 7x)(2x + -3) Reorder the terms: 0 = (5 + 7x)(-3 + 2x) Multiply (5 + 7x) * (-3 + 2x) 0 = (5(-3 + 2x) + 7x * (-3 + 2x)) 0 = ((-3 * 5 + 2x * 5) + 7x * (-3 + 2x)) 0 = ((-15 + 10x) + 7x * (-3 + 2x)) 0 = (-15 + 10x + (-3 * 7x + 2x * 7x)) 0 = (-15 + 10x + (-21x + 14x2)) Combine like terms: 10x + -21x = -11x 0 = (-15 + -11x + 14x2) Solving 0 = -15 + -11x + 14x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + 11x + -14x2 = -15 + -11x + 14x2 + 15 + 11x + -14x2 Reorder the terms: 15 + 11x + -14x2 = -15 + 15 + -11x + 11x + 14x2 + -14x2 Combine like terms: -15 + 15 = 0 15 + 11x + -14x2 = 0 + -11x + 11x + 14x2 + -14x2 15 + 11x + -14x2 = -11x + 11x + 14x2 + -14x2 Combine like terms: -11x + 11x = 0 15 + 11x + -14x2 = 0 + 14x2 + -14x2 15 + 11x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 15 + 11x + -14x2 = 0 Factor a trinomial. (3 + -2x)(5 + 7x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(5 + 7x)' equal to zero and attempt to solve: Simplifying 5 + 7x = 0 Solving 5 + 7x = 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 + 7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x = 0 + -5 7x = 0 + -5 Combine like terms: 0 + -5 = -5 7x = -5 Divide each side by '7'. x = -0.7142857143 Simplifying x = -0.7142857143Solution
x = {1.5, -0.7142857143}
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