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Simplifying (2x + 1)(3x + -5) = 0 Reorder the terms: (1 + 2x)(3x + -5) = 0 Reorder the terms: (1 + 2x)(-5 + 3x) = 0 Multiply (1 + 2x) * (-5 + 3x) (1(-5 + 3x) + 2x * (-5 + 3x)) = 0 ((-5 * 1 + 3x * 1) + 2x * (-5 + 3x)) = 0 ((-5 + 3x) + 2x * (-5 + 3x)) = 0 (-5 + 3x + (-5 * 2x + 3x * 2x)) = 0 (-5 + 3x + (-10x + 6x2)) = 0 Combine like terms: 3x + -10x = -7x (-5 + -7x + 6x2) = 0 Solving -5 + -7x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -2x)(5 + -3x) = 0Subproblem 1
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 = -0.5Subproblem 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 = {-0.5, 1.666666667}
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