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Simplifying (5 + -2x)(3x + 1) = 0 Reorder the terms: (5 + -2x)(1 + 3x) = 0 Multiply (5 + -2x) * (1 + 3x) (5(1 + 3x) + -2x * (1 + 3x)) = 0 ((1 * 5 + 3x * 5) + -2x * (1 + 3x)) = 0 ((5 + 15x) + -2x * (1 + 3x)) = 0 (5 + 15x + (1 * -2x + 3x * -2x)) = 0 (5 + 15x + (-2x + -6x2)) = 0 Combine like terms: 15x + -2x = 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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