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Simplifying (6x + 3)(4x + -6) = 0 Reorder the terms: (3 + 6x)(4x + -6) = 0 Reorder the terms: (3 + 6x)(-6 + 4x) = 0 Multiply (3 + 6x) * (-6 + 4x) (3(-6 + 4x) + 6x * (-6 + 4x)) = 0 ((-6 * 3 + 4x * 3) + 6x * (-6 + 4x)) = 0 ((-18 + 12x) + 6x * (-6 + 4x)) = 0 (-18 + 12x + (-6 * 6x + 4x * 6x)) = 0 (-18 + 12x + (-36x + 24x2)) = 0 Combine like terms: 12x + -36x = -24x (-18 + -24x + 24x2) = 0 Solving -18 + -24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -4x + 4x2) = 0 Factor a trinomial. 6((-1 + -2x)(3 + -2x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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 = {-0.5, 1.5}
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