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Simplifying 0 = (15x + 2)(x + 7) Reorder the terms: 0 = (2 + 15x)(x + 7) Reorder the terms: 0 = (2 + 15x)(7 + x) Multiply (2 + 15x) * (7 + x) 0 = (2(7 + x) + 15x * (7 + x)) 0 = ((7 * 2 + x * 2) + 15x * (7 + x)) 0 = ((14 + 2x) + 15x * (7 + x)) 0 = (14 + 2x + (7 * 15x + x * 15x)) 0 = (14 + 2x + (105x + 15x2)) Combine like terms: 2x + 105x = 107x 0 = (14 + 107x + 15x2) Solving 0 = 14 + 107x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + -107x + -15x2 = 14 + 107x + 15x2 + -14 + -107x + -15x2 Reorder the terms: -14 + -107x + -15x2 = 14 + -14 + 107x + -107x + 15x2 + -15x2 Combine like terms: 14 + -14 = 0 -14 + -107x + -15x2 = 0 + 107x + -107x + 15x2 + -15x2 -14 + -107x + -15x2 = 107x + -107x + 15x2 + -15x2 Combine like terms: 107x + -107x = 0 -14 + -107x + -15x2 = 0 + 15x2 + -15x2 -14 + -107x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -14 + -107x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 107x + 15x2) = 0 Factor a trinomial. -1((7 + x)(2 + 15x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(2 + 15x)' equal to zero and attempt to solve: Simplifying 2 + 15x = 0 Solving 2 + 15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 15x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 15x = 0 + -2 15x = 0 + -2 Combine like terms: 0 + -2 = -2 15x = -2 Divide each side by '15'. x = -0.1333333333 Simplifying x = -0.1333333333Solution
x = {-7, -0.1333333333}
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