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Simplifying (5x + 6)(6x + -3) = 0 Reorder the terms: (6 + 5x)(6x + -3) = 0 Reorder the terms: (6 + 5x)(-3 + 6x) = 0 Multiply (6 + 5x) * (-3 + 6x) (6(-3 + 6x) + 5x * (-3 + 6x)) = 0 ((-3 * 6 + 6x * 6) + 5x * (-3 + 6x)) = 0 ((-18 + 36x) + 5x * (-3 + 6x)) = 0 (-18 + 36x + (-3 * 5x + 6x * 5x)) = 0 (-18 + 36x + (-15x + 30x2)) = 0 Combine like terms: 36x + -15x = 21x (-18 + 21x + 30x2) = 0 Solving -18 + 21x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 7x + 10x2) = 0 Factor a trinomial. 3((-6 + -5x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 2
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 = 0.5Solution
x = {-1.2, 0.5}
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