6v(6v+6)-5=1+6v

Solution for 6v(6v+6)-5=1+6v equation:

Simplifying
6v(6v + 6) + -5 = 1 + 6v

Reorder the terms:
6v(6 + 6v) + -5 = 1 + 6v
(6 * 6v + 6v * 6v) + -5 = 1 + 6v
(36v + 36v2) + -5 = 1 + 6v

Reorder the terms:
-5 + 36v + 36v2 = 1 + 6v

Solving
-5 + 36v + 36v2 = 1 + 6v

Solving for variable 'v'.

Reorder the terms:
-5 + -1 + 36v + -6v + 36v2 = 1 + 6v + -1 + -6v

Combine like terms: -5 + -1 = -6
-6 + 36v + -6v + 36v2 = 1 + 6v + -1 + -6v

Combine like terms: 36v + -6v = 30v
-6 + 30v + 36v2 = 1 + 6v + -1 + -6v

Reorder the terms:
-6 + 30v + 36v2 = 1 + -1 + 6v + -6v

Combine like terms: 1 + -1 = 0
-6 + 30v + 36v2 = 0 + 6v + -6v
-6 + 30v + 36v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
-6 + 30v + 36v2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 5v + 6v2) = 0

Factor a trinomial.
6((-1 + -1v)(1 + -6v)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -6v)' equal to zero and attempt to solve:

Simplifying
1 + -6v = 0

Solving
1 + -6v = 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 + -6v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6v = 0 + -1
-6v = 0 + -1

Combine like terms: 0 + -1 = -1
-6v = -1

Divide each side by '-6'.
v = 0.1666666667

Simplifying
v = 0.1666666667
Solution
v = {-1, 0.1666666667}