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Simplifying 0 = (12x + -2)(6x + 5) Reorder the terms: 0 = (-2 + 12x)(6x + 5) Reorder the terms: 0 = (-2 + 12x)(5 + 6x) Multiply (-2 + 12x) * (5 + 6x) 0 = (-2(5 + 6x) + 12x * (5 + 6x)) 0 = ((5 * -2 + 6x * -2) + 12x * (5 + 6x)) 0 = ((-10 + -12x) + 12x * (5 + 6x)) 0 = (-10 + -12x + (5 * 12x + 6x * 12x)) 0 = (-10 + -12x + (60x + 72x2)) Combine like terms: -12x + 60x = 48x 0 = (-10 + 48x + 72x2) Solving 0 = -10 + 48x + 72x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -48x + -72x2 = -10 + 48x + 72x2 + 10 + -48x + -72x2 Reorder the terms: 10 + -48x + -72x2 = -10 + 10 + 48x + -48x + 72x2 + -72x2 Combine like terms: -10 + 10 = 0 10 + -48x + -72x2 = 0 + 48x + -48x + 72x2 + -72x2 10 + -48x + -72x2 = 48x + -48x + 72x2 + -72x2 Combine like terms: 48x + -48x = 0 10 + -48x + -72x2 = 0 + 72x2 + -72x2 10 + -48x + -72x2 = 72x2 + -72x2 Combine like terms: 72x2 + -72x2 = 0 10 + -48x + -72x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -24x + -36x2) = 0 Factor a trinomial. 2((1 + -6x)(5 + 6x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Divide each side by '-6'. x = 0.1666666667 Simplifying x = 0.1666666667Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {0.1666666667, -0.8333333333}
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