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Simplifying (12x + -2)(4x + -6) = 0 Reorder the terms: (-2 + 12x)(4x + -6) = 0 Reorder the terms: (-2 + 12x)(-6 + 4x) = 0 Multiply (-2 + 12x) * (-6 + 4x) (-2(-6 + 4x) + 12x * (-6 + 4x)) = 0 ((-6 * -2 + 4x * -2) + 12x * (-6 + 4x)) = 0 ((12 + -8x) + 12x * (-6 + 4x)) = 0 (12 + -8x + (-6 * 12x + 4x * 12x)) = 0 (12 + -8x + (-72x + 48x2)) = 0 Combine like terms: -8x + -72x = -80x (12 + -80x + 48x2) = 0 Solving 12 + -80x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -20x + 12x2) = 0 Factor a trinomial. 4((1 + -6x)(3 + -2x)) = 0 Ignore the factor 4.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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0.1666666667, 1.5}
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