2v^2-24v+70=v^2-14v+49

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Solution for 2v^2-24v+70=v^2-14v+49 equation: 


Simplifying
2v2 + -24v + 70 = v2 + -14v + 49

Reorder the terms:
70 + -24v + 2v2 = v2 + -14v + 49

Reorder the terms:
70 + -24v + 2v2 = 49 + -14v + v2

Solving
70 + -24v + 2v2 = 49 + -14v + v2

Solving for variable 'v'.

Reorder the terms:
70 + -49 + -24v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 70 + -49 = 21
21 + -24v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: -24v + 14v = -10v
21 + -10v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
21 + -10v + 1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Reorder the terms:
21 + -10v + 1v2 = 49 + -49 + -14v + 14v + v2 + -1v2

Combine like terms: 49 + -49 = 0
21 + -10v + 1v2 = 0 + -14v + 14v + v2 + -1v2
21 + -10v + 1v2 = -14v + 14v + v2 + -1v2

Combine like terms: -14v + 14v = 0
21 + -10v + 1v2 = 0 + v2 + -1v2
21 + -10v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
21 + -10v + 1v2 = 0

Factor a trinomial.
(3 + -1v)(7 + -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 '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {3, 7}

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