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Simplifying (3x + -1)(2x + 5) = 0 Reorder the terms: (-1 + 3x)(2x + 5) = 0 Reorder the terms: (-1 + 3x)(5 + 2x) = 0 Multiply (-1 + 3x) * (5 + 2x) (-1(5 + 2x) + 3x * (5 + 2x)) = 0 ((5 * -1 + 2x * -1) + 3x * (5 + 2x)) = 0 ((-5 + -2x) + 3x * (5 + 2x)) = 0 (-5 + -2x + (5 * 3x + 2x * 3x)) = 0 (-5 + -2x + (15x + 6x2)) = 0 Combine like terms: -2x + 15x = 13x (-5 + 13x + 6x2) = 0 Solving -5 + 13x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -2x)(1 + -3x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, 0.3333333333}
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