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Simplifying (3x + 1)(2x + -5) = 39 Reorder the terms: (1 + 3x)(2x + -5) = 39 Reorder the terms: (1 + 3x)(-5 + 2x) = 39 Multiply (1 + 3x) * (-5 + 2x) (1(-5 + 2x) + 3x * (-5 + 2x)) = 39 ((-5 * 1 + 2x * 1) + 3x * (-5 + 2x)) = 39 ((-5 + 2x) + 3x * (-5 + 2x)) = 39 (-5 + 2x + (-5 * 3x + 2x * 3x)) = 39 (-5 + 2x + (-15x + 6x2)) = 39 Combine like terms: 2x + -15x = -13x (-5 + -13x + 6x2) = 39 Solving -5 + -13x + 6x2 = 39 Solving for variable 'x'. Reorder the terms: -5 + -39 + -13x + 6x2 = 39 + -39 Combine like terms: -5 + -39 = -44 -44 + -13x + 6x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -44 + -13x + 6x2 = 0 Factor a trinomial. (-11 + -6x)(4 + -1x) = 0Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve: Simplifying -11 + -6x = 0 Solving -11 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -6x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6x = 0 + 11 -6x = 0 + 11 Combine like terms: 0 + 11 = 11 -6x = 11 Divide each side by '-6'. x = -1.833333333 Simplifying x = -1.833333333Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-1.833333333, 4}
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