(3v-3)(4v+1)=5v^2-32v-21

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Solution for (3v-3)(4v+1)=5v^2-32v-21 equation: 


Simplifying
(3v + -3)(4v + 1) = 5v2 + -32v + -21

Reorder the terms:
(-3 + 3v)(4v + 1) = 5v2 + -32v + -21

Reorder the terms:
(-3 + 3v)(1 + 4v) = 5v2 + -32v + -21

Multiply (-3 + 3v) * (1 + 4v)
(-3(1 + 4v) + 3v * (1 + 4v)) = 5v2 + -32v + -21
((1 * -3 + 4v * -3) + 3v * (1 + 4v)) = 5v2 + -32v + -21
((-3 + -12v) + 3v * (1 + 4v)) = 5v2 + -32v + -21
(-3 + -12v + (1 * 3v + 4v * 3v)) = 5v2 + -32v + -21
(-3 + -12v + (3v + 12v2)) = 5v2 + -32v + -21

Combine like terms: -12v + 3v = -9v
(-3 + -9v + 12v2) = 5v2 + -32v + -21

Reorder the terms:
-3 + -9v + 12v2 = -21 + -32v + 5v2

Solving
-3 + -9v + 12v2 = -21 + -32v + 5v2

Solving for variable 'v'.

Reorder the terms:
-3 + 21 + -9v + 32v + 12v2 + -5v2 = -21 + -32v + 5v2 + 21 + 32v + -5v2

Combine like terms: -3 + 21 = 18
18 + -9v + 32v + 12v2 + -5v2 = -21 + -32v + 5v2 + 21 + 32v + -5v2

Combine like terms: -9v + 32v = 23v
18 + 23v + 12v2 + -5v2 = -21 + -32v + 5v2 + 21 + 32v + -5v2

Combine like terms: 12v2 + -5v2 = 7v2
18 + 23v + 7v2 = -21 + -32v + 5v2 + 21 + 32v + -5v2

Reorder the terms:
18 + 23v + 7v2 = -21 + 21 + -32v + 32v + 5v2 + -5v2

Combine like terms: -21 + 21 = 0
18 + 23v + 7v2 = 0 + -32v + 32v + 5v2 + -5v2
18 + 23v + 7v2 = -32v + 32v + 5v2 + -5v2

Combine like terms: -32v + 32v = 0
18 + 23v + 7v2 = 0 + 5v2 + -5v2
18 + 23v + 7v2 = 5v2 + -5v2

Combine like terms: 5v2 + -5v2 = 0
18 + 23v + 7v2 = 0

Factor a trinomial.
(2 + v)(9 + 7v) = 0


Subproblem 1
Set the factor '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

Simplifying
v = -2

Subproblem 2
Set the factor '(9 + 7v)' equal to zero and attempt to solve:

Simplifying
9 + 7v = 0

Solving
9 + 7v = 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 + 7v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7v = 0 + -9
7v = 0 + -9

Combine like terms: 0 + -9 = -9
7v = -9

Divide each side by '7'.
v = -1.285714286

Simplifying
v = -1.285714286
Solution
v = {-2, -1.285714286}

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