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Simplifying (4x + 5)(x + 1) = 14 Reorder the terms: (5 + 4x)(x + 1) = 14 Reorder the terms: (5 + 4x)(1 + x) = 14 Multiply (5 + 4x) * (1 + x) (5(1 + x) + 4x * (1 + x)) = 14 ((1 * 5 + x * 5) + 4x * (1 + x)) = 14 ((5 + 5x) + 4x * (1 + x)) = 14 (5 + 5x + (1 * 4x + x * 4x)) = 14 (5 + 5x + (4x + 4x2)) = 14 Combine like terms: 5x + 4x = 9x (5 + 9x + 4x2) = 14 Solving 5 + 9x + 4x2 = 14 Solving for variable 'x'. Reorder the terms: 5 + -14 + 9x + 4x2 = 14 + -14 Combine like terms: 5 + -14 = -9 -9 + 9x + 4x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -9 + 9x + 4x2 = 0 Factor a trinomial. (-3 + -1x)(3 + -4x) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {-3, 0.75}
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