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Simplifying 0 = 2(9x + 6)(7x + 3) Reorder the terms: 0 = 2(6 + 9x)(7x + 3) Reorder the terms: 0 = 2(6 + 9x)(3 + 7x) Multiply (6 + 9x) * (3 + 7x) 0 = 2(6(3 + 7x) + 9x * (3 + 7x)) 0 = 2((3 * 6 + 7x * 6) + 9x * (3 + 7x)) 0 = 2((18 + 42x) + 9x * (3 + 7x)) 0 = 2(18 + 42x + (3 * 9x + 7x * 9x)) 0 = 2(18 + 42x + (27x + 63x2)) Combine like terms: 42x + 27x = 69x 0 = 2(18 + 69x + 63x2) 0 = (18 * 2 + 69x * 2 + 63x2 * 2) 0 = (36 + 138x + 126x2) Solving 0 = 36 + 138x + 126x2 Solving for variable 'x'. Combine like terms: 0 + -36 = -36 -36 + -138x + -126x2 = 36 + 138x + 126x2 + -36 + -138x + -126x2 Reorder the terms: -36 + -138x + -126x2 = 36 + -36 + 138x + -138x + 126x2 + -126x2 Combine like terms: 36 + -36 = 0 -36 + -138x + -126x2 = 0 + 138x + -138x + 126x2 + -126x2 -36 + -138x + -126x2 = 138x + -138x + 126x2 + -126x2 Combine like terms: 138x + -138x = 0 -36 + -138x + -126x2 = 0 + 126x2 + -126x2 -36 + -138x + -126x2 = 126x2 + -126x2 Combine like terms: 126x2 + -126x2 = 0 -36 + -138x + -126x2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(6 + 23x + 21x2) = 0 Factor a trinomial. -6((2 + 3x)(3 + 7x)) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 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 = {-0.6666666667, -0.4285714286}
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