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Simplifying (3x + -2)(5x + -7) = 0 Reorder the terms: (-2 + 3x)(5x + -7) = 0 Reorder the terms: (-2 + 3x)(-7 + 5x) = 0 Multiply (-2 + 3x) * (-7 + 5x) (-2(-7 + 5x) + 3x * (-7 + 5x)) = 0 ((-7 * -2 + 5x * -2) + 3x * (-7 + 5x)) = 0 ((14 + -10x) + 3x * (-7 + 5x)) = 0 (14 + -10x + (-7 * 3x + 5x * 3x)) = 0 (14 + -10x + (-21x + 15x^{2})) = 0 Combine like terms: -10x + -21x = -31x (14 + -31x + 15x^{2}) = 0 Solving 14 + -31x + 15x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (2 + -3x)(7 + -5x) = 0## Subproblem 1

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 = 0.6666666667## Subproblem 2

Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4## Solution

x = {0.6666666667, 1.4}

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