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Simplifying (3x + 5)(-6x + 4) = 0 Reorder the terms: (5 + 3x)(-6x + 4) = 0 Reorder the terms: (5 + 3x)(4 + -6x) = 0 Multiply (5 + 3x) * (4 + -6x) (5(4 + -6x) + 3x * (4 + -6x)) = 0 ((4 * 5 + -6x * 5) + 3x * (4 + -6x)) = 0 ((20 + -30x) + 3x * (4 + -6x)) = 0 (20 + -30x + (4 * 3x + -6x * 3x)) = 0 (20 + -30x + (12x + -18x2)) = 0 Combine like terms: -30x + 12x = -18x (20 + -18x + -18x2) = 0 Solving 20 + -18x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -9x + -9x2) = 0 Factor a trinomial. 2((2 + -3x)(5 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {0.6666666667, -1.666666667}
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