-7v^2+4v+2=-8v^2+7

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Solution for -7v^2+4v+2=-8v^2+7 equation: 


Simplifying
-7v2 + 4v + 2 = -8v2 + 7

Reorder the terms:
2 + 4v + -7v2 = -8v2 + 7

Reorder the terms:
2 + 4v + -7v2 = 7 + -8v2

Solving
2 + 4v + -7v2 = 7 + -8v2

Solving for variable 'v'.

Reorder the terms:
2 + -7 + 4v + -7v2 + 8v2 = 7 + -8v2 + -7 + 8v2

Combine like terms: 2 + -7 = -5
-5 + 4v + -7v2 + 8v2 = 7 + -8v2 + -7 + 8v2

Combine like terms: -7v2 + 8v2 = 1v2
-5 + 4v + 1v2 = 7 + -8v2 + -7 + 8v2

Reorder the terms:
-5 + 4v + 1v2 = 7 + -7 + -8v2 + 8v2

Combine like terms: 7 + -7 = 0
-5 + 4v + 1v2 = 0 + -8v2 + 8v2
-5 + 4v + 1v2 = -8v2 + 8v2

Combine like terms: -8v2 + 8v2 = 0
-5 + 4v + 1v2 = 0

Factor a trinomial.
(-5 + -1v)(1 + -1v) = 0


Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {-5, 1}

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