2v^2-13v+24=v^2-12v+36

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Solution for 2v^2-13v+24=v^2-12v+36 equation: 


Simplifying
2v2 + -13v + 24 = v2 + -12v + 36

Reorder the terms:
24 + -13v + 2v2 = v2 + -12v + 36

Reorder the terms:
24 + -13v + 2v2 = 36 + -12v + v2

Solving
24 + -13v + 2v2 = 36 + -12v + v2

Solving for variable 'v'.

Reorder the terms:
24 + -36 + -13v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 24 + -36 = -12
-12 + -13v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: -13v + 12v = -1v
-12 + -1v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-12 + -1v + 1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Reorder the terms:
-12 + -1v + 1v2 = 36 + -36 + -12v + 12v + v2 + -1v2

Combine like terms: 36 + -36 = 0
-12 + -1v + 1v2 = 0 + -12v + 12v + v2 + -1v2
-12 + -1v + 1v2 = -12v + 12v + v2 + -1v2

Combine like terms: -12v + 12v = 0
-12 + -1v + 1v2 = 0 + v2 + -1v2
-12 + -1v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-12 + -1v + 1v2 = 0

Factor a trinomial.
(-3 + -1v)(4 + -1v) = 0


Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve:

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 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 + -1v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1v = 0 + 3
-1v = 0 + 3

Combine like terms: 0 + 3 = 3
-1v = 3

Divide each side by '-1'.
v = -3

Simplifying
v = -3

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-3, 4}

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