7v^2-23=6v-7

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Solution for 7v^2-23=6v-7 equation: 


Simplifying
7v2 + -23 = 6v + -7

Reorder the terms:
-23 + 7v2 = 6v + -7

Reorder the terms:
-23 + 7v2 = -7 + 6v

Solving
-23 + 7v2 = -7 + 6v

Solving for variable 'v'.

Reorder the terms:
-23 + 7 + -6v + 7v2 = -7 + 6v + 7 + -6v

Combine like terms: -23 + 7 = -16
-16 + -6v + 7v2 = -7 + 6v + 7 + -6v

Reorder the terms:
-16 + -6v + 7v2 = -7 + 7 + 6v + -6v

Combine like terms: -7 + 7 = 0
-16 + -6v + 7v2 = 0 + 6v + -6v
-16 + -6v + 7v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
-16 + -6v + 7v2 = 0

Factor a trinomial.
(-8 + -7v)(2 + -1v) = 0


Subproblem 1
Set the factor '(-8 + -7v)' equal to zero and attempt to solve:

Simplifying
-8 + -7v = 0

Solving
-8 + -7v = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7v = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7v = 0 + 8
-7v = 0 + 8

Combine like terms: 0 + 8 = 8
-7v = 8

Divide each side by '-7'.
v = -1.142857143

Simplifying
v = -1.142857143

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 = {-1.142857143, 2}

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