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Simplifying (3x + 1)(5x + -1) = 0 Reorder the terms: (1 + 3x)(5x + -1) = 0 Reorder the terms: (1 + 3x)(-1 + 5x) = 0 Multiply (1 + 3x) * (-1 + 5x) (1(-1 + 5x) + 3x * (-1 + 5x)) = 0 ((-1 * 1 + 5x * 1) + 3x * (-1 + 5x)) = 0 ((-1 + 5x) + 3x * (-1 + 5x)) = 0 (-1 + 5x + (-1 * 3x + 5x * 3x)) = 0 (-1 + 5x + (-3x + 15x2)) = 0 Combine like terms: 5x + -3x = 2x (-1 + 2x + 15x2) = 0 Solving -1 + 2x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -3x)(1 + -5x) = 0Subproblem 1
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 = -0.3333333333Subproblem 2
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 = 0.2Solution
x = {-0.3333333333, 0.2}
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