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Simplifying (5x + -3)(3x + -1) = 5x + -3 Reorder the terms: (-3 + 5x)(3x + -1) = 5x + -3 Reorder the terms: (-3 + 5x)(-1 + 3x) = 5x + -3 Multiply (-3 + 5x) * (-1 + 3x) (-3(-1 + 3x) + 5x * (-1 + 3x)) = 5x + -3 ((-1 * -3 + 3x * -3) + 5x * (-1 + 3x)) = 5x + -3 ((3 + -9x) + 5x * (-1 + 3x)) = 5x + -3 (3 + -9x + (-1 * 5x + 3x * 5x)) = 5x + -3 (3 + -9x + (-5x + 15x2)) = 5x + -3 Combine like terms: -9x + -5x = -14x (3 + -14x + 15x2) = 5x + -3 Reorder the terms: 3 + -14x + 15x2 = -3 + 5x Solving 3 + -14x + 15x2 = -3 + 5x Solving for variable 'x'. Reorder the terms: 3 + 3 + -14x + -5x + 15x2 = -3 + 5x + 3 + -5x Combine like terms: 3 + 3 = 6 6 + -14x + -5x + 15x2 = -3 + 5x + 3 + -5x Combine like terms: -14x + -5x = -19x 6 + -19x + 15x2 = -3 + 5x + 3 + -5x Reorder the terms: 6 + -19x + 15x2 = -3 + 3 + 5x + -5x Combine like terms: -3 + 3 = 0 6 + -19x + 15x2 = 0 + 5x + -5x 6 + -19x + 15x2 = 5x + -5x Combine like terms: 5x + -5x = 0 6 + -19x + 15x2 = 0 Factor a trinomial. (3 + -5x)(2 + -3x) = 0Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0.6, 0.6666666667}
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