4v^2+6v-7=4v+3v^2+1

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Solution for 4v^2+6v-7=4v+3v^2+1 equation: 


Simplifying
4v2 + 6v + -7 = 4v + 3v2 + 1

Reorder the terms:
-7 + 6v + 4v2 = 4v + 3v2 + 1

Reorder the terms:
-7 + 6v + 4v2 = 1 + 4v + 3v2

Solving
-7 + 6v + 4v2 = 1 + 4v + 3v2

Solving for variable 'v'.

Reorder the terms:
-7 + -1 + 6v + -4v + 4v2 + -3v2 = 1 + 4v + 3v2 + -1 + -4v + -3v2

Combine like terms: -7 + -1 = -8
-8 + 6v + -4v + 4v2 + -3v2 = 1 + 4v + 3v2 + -1 + -4v + -3v2

Combine like terms: 6v + -4v = 2v
-8 + 2v + 4v2 + -3v2 = 1 + 4v + 3v2 + -1 + -4v + -3v2

Combine like terms: 4v2 + -3v2 = 1v2
-8 + 2v + 1v2 = 1 + 4v + 3v2 + -1 + -4v + -3v2

Reorder the terms:
-8 + 2v + 1v2 = 1 + -1 + 4v + -4v + 3v2 + -3v2

Combine like terms: 1 + -1 = 0
-8 + 2v + 1v2 = 0 + 4v + -4v + 3v2 + -3v2
-8 + 2v + 1v2 = 4v + -4v + 3v2 + -3v2

Combine like terms: 4v + -4v = 0
-8 + 2v + 1v2 = 0 + 3v2 + -3v2
-8 + 2v + 1v2 = 3v2 + -3v2

Combine like terms: 3v2 + -3v2 = 0
-8 + 2v + 1v2 = 0

Factor a trinomial.
(-4 + -1v)(2 + -1v) = 0


Subproblem 1
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

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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 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 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-4, 2}

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