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Simplifying 4x^{2}+ 13x + -75 = 0 Reorder the terms: -75 + 13x + 4x^{2}= 0 Solving -75 + 13x + 4x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (-25 + -4x)(3 + -1x) = 0## Subproblem 1

Set the factor '(-25 + -4x)' equal to zero and attempt to solve: Simplifying -25 + -4x = 0 Solving -25 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -4x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4x = 0 + 25 -4x = 0 + 25 Combine like terms: 0 + 25 = 25 -4x = 25 Divide each side by '-4'. x = -6.25 Simplifying x = -6.25## Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3## Solution

x = {-6.25, 3}

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