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Simplifying (2x + 3)(6x + -2) = 0 Reorder the terms: (3 + 2x)(6x + -2) = 0 Reorder the terms: (3 + 2x)(-2 + 6x) = 0 Multiply (3 + 2x) * (-2 + 6x) (3(-2 + 6x) + 2x * (-2 + 6x)) = 0 ((-2 * 3 + 6x * 3) + 2x * (-2 + 6x)) = 0 ((-6 + 18x) + 2x * (-2 + 6x)) = 0 (-6 + 18x + (-2 * 2x + 6x * 2x)) = 0 (-6 + 18x + (-4x + 12x2)) = 0 Combine like terms: 18x + -4x = 14x (-6 + 14x + 12x2) = 0 Solving -6 + 14x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 7x + 6x2) = 0 Factor a trinomial. 2((-3 + -2x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-1.5, 0.3333333333}
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