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Simplifying (4v + -5)(3v + 1) = 8v2 + -32v + -32 Reorder the terms: (-5 + 4v)(3v + 1) = 8v2 + -32v + -32 Reorder the terms: (-5 + 4v)(1 + 3v) = 8v2 + -32v + -32 Multiply (-5 + 4v) * (1 + 3v) (-5(1 + 3v) + 4v * (1 + 3v)) = 8v2 + -32v + -32 ((1 * -5 + 3v * -5) + 4v * (1 + 3v)) = 8v2 + -32v + -32 ((-5 + -15v) + 4v * (1 + 3v)) = 8v2 + -32v + -32 (-5 + -15v + (1 * 4v + 3v * 4v)) = 8v2 + -32v + -32 (-5 + -15v + (4v + 12v2)) = 8v2 + -32v + -32 Combine like terms: -15v + 4v = -11v (-5 + -11v + 12v2) = 8v2 + -32v + -32 Reorder the terms: -5 + -11v + 12v2 = -32 + -32v + 8v2 Solving -5 + -11v + 12v2 = -32 + -32v + 8v2 Solving for variable 'v'. Reorder the terms: -5 + 32 + -11v + 32v + 12v2 + -8v2 = -32 + -32v + 8v2 + 32 + 32v + -8v2 Combine like terms: -5 + 32 = 27 27 + -11v + 32v + 12v2 + -8v2 = -32 + -32v + 8v2 + 32 + 32v + -8v2 Combine like terms: -11v + 32v = 21v 27 + 21v + 12v2 + -8v2 = -32 + -32v + 8v2 + 32 + 32v + -8v2 Combine like terms: 12v2 + -8v2 = 4v2 27 + 21v + 4v2 = -32 + -32v + 8v2 + 32 + 32v + -8v2 Reorder the terms: 27 + 21v + 4v2 = -32 + 32 + -32v + 32v + 8v2 + -8v2 Combine like terms: -32 + 32 = 0 27 + 21v + 4v2 = 0 + -32v + 32v + 8v2 + -8v2 27 + 21v + 4v2 = -32v + 32v + 8v2 + -8v2 Combine like terms: -32v + 32v = 0 27 + 21v + 4v2 = 0 + 8v2 + -8v2 27 + 21v + 4v2 = 8v2 + -8v2 Combine like terms: 8v2 + -8v2 = 0 27 + 21v + 4v2 = 0 Factor a trinomial. (3 + v)(9 + 4v) = 0Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(9 + 4v)' equal to zero and attempt to solve: Simplifying 9 + 4v = 0 Solving 9 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4v = 0 + -9 4v = 0 + -9 Combine like terms: 0 + -9 = -9 4v = -9 Divide each side by '4'. v = -2.25 Simplifying v = -2.25Solution
v = {-3, -2.25}
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