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Simplifying (7x + 5)(-7x + -2) = 3(7x + 5) Reorder the terms: (5 + 7x)(-7x + -2) = 3(7x + 5) Reorder the terms: (5 + 7x)(-2 + -7x) = 3(7x + 5) Multiply (5 + 7x) * (-2 + -7x) (5(-2 + -7x) + 7x * (-2 + -7x)) = 3(7x + 5) ((-2 * 5 + -7x * 5) + 7x * (-2 + -7x)) = 3(7x + 5) ((-10 + -35x) + 7x * (-2 + -7x)) = 3(7x + 5) (-10 + -35x + (-2 * 7x + -7x * 7x)) = 3(7x + 5) (-10 + -35x + (-14x + -49x2)) = 3(7x + 5) Combine like terms: -35x + -14x = -49x (-10 + -49x + -49x2) = 3(7x + 5) Reorder the terms: -10 + -49x + -49x2 = 3(5 + 7x) -10 + -49x + -49x2 = (5 * 3 + 7x * 3) -10 + -49x + -49x2 = (15 + 21x) Solving -10 + -49x + -49x2 = 15 + 21x Solving for variable 'x'. Reorder the terms: -10 + -15 + -49x + -21x + -49x2 = 15 + 21x + -15 + -21x Combine like terms: -10 + -15 = -25 -25 + -49x + -21x + -49x2 = 15 + 21x + -15 + -21x Combine like terms: -49x + -21x = -70x -25 + -70x + -49x2 = 15 + 21x + -15 + -21x Reorder the terms: -25 + -70x + -49x2 = 15 + -15 + 21x + -21x Combine like terms: 15 + -15 = 0 -25 + -70x + -49x2 = 0 + 21x + -21x -25 + -70x + -49x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -25 + -70x + -49x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 70x + 49x2) = 0 Factor a trinomial. -1((5 + 7x)(5 + 7x)) = 0 Ignore the factor -1.Subproblem 1
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 = -0.7142857143Subproblem 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 = {-0.7142857143, -0.7142857143}
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