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Simplifying (4x + -5)(7 + x) = 0 Reorder the terms: (-5 + 4x)(7 + x) = 0 Multiply (-5 + 4x) * (7 + x) (-5(7 + x) + 4x * (7 + x)) = 0 ((7 * -5 + x * -5) + 4x * (7 + x)) = 0 ((-35 + -5x) + 4x * (7 + x)) = 0 (-35 + -5x + (7 * 4x + x * 4x)) = 0 (-35 + -5x + (28x + 4x^{2})) = 0 Combine like terms: -5x + 28x = 23x (-35 + 23x + 4x^{2}) = 0 Solving -35 + 23x + 4x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (-7 + -1x)(5 + -4x) = 0## Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7## Subproblem 2

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25## Solution

x = {-7, 1.25}

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