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Simplifying 0 = (3x + 7)(7x + 3) Reorder the terms: 0 = (7 + 3x)(7x + 3) Reorder the terms: 0 = (7 + 3x)(3 + 7x) Multiply (7 + 3x) * (3 + 7x) 0 = (7(3 + 7x) + 3x * (3 + 7x)) 0 = ((3 * 7 + 7x * 7) + 3x * (3 + 7x)) 0 = ((21 + 49x) + 3x * (3 + 7x)) 0 = (21 + 49x + (3 * 3x + 7x * 3x)) 0 = (21 + 49x + (9x + 21x2)) Combine like terms: 49x + 9x = 58x 0 = (21 + 58x + 21x2) Solving 0 = 21 + 58x + 21x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + -58x + -21x2 = 21 + 58x + 21x2 + -21 + -58x + -21x2 Reorder the terms: -21 + -58x + -21x2 = 21 + -21 + 58x + -58x + 21x2 + -21x2 Combine like terms: 21 + -21 = 0 -21 + -58x + -21x2 = 0 + 58x + -58x + 21x2 + -21x2 -21 + -58x + -21x2 = 58x + -58x + 21x2 + -21x2 Combine like terms: 58x + -58x = 0 -21 + -58x + -21x2 = 0 + 21x2 + -21x2 -21 + -58x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 -21 + -58x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 58x + 21x2) = 0 Factor a trinomial. -1((7 + 3x)(3 + 7x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 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 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve: Simplifying 3 + 7x = 0 Solving 3 + 7x = 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 + 7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x = 0 + -3 7x = 0 + -3 Combine like terms: 0 + -3 = -3 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286Solution
x = {-2.333333333, -0.4285714286}
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