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Simplifying (5x + 1)(2x + -3) = 0 Reorder the terms: (1 + 5x)(2x + -3) = 0 Reorder the terms: (1 + 5x)(-3 + 2x) = 0 Multiply (1 + 5x) * (-3 + 2x) (1(-3 + 2x) + 5x * (-3 + 2x)) = 0 ((-3 * 1 + 2x * 1) + 5x * (-3 + 2x)) = 0 ((-3 + 2x) + 5x * (-3 + 2x)) = 0 (-3 + 2x + (-3 * 5x + 2x * 5x)) = 0 (-3 + 2x + (-15x + 10x2)) = 0 Combine like terms: 2x + -15x = -13x (-3 + -13x + 10x2) = 0 Solving -3 + -13x + 10x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -5x)(3 + -2x) = 0Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 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 = {-0.2, 1.5}
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