11b^2-12b-1=b-4+7b^2

Solution for 11b^2-12b-1=b-4+7b^2 equation:

Simplifying
11b2 + -12b + -1 = b + -4 + 7b2

Reorder the terms:
-1 + -12b + 11b2 = b + -4 + 7b2

Reorder the terms:
-1 + -12b + 11b2 = -4 + b + 7b2

Solving
-1 + -12b + 11b2 = -4 + b + 7b2

Solving for variable 'b'.

Reorder the terms:
-1 + 4 + -12b + -1b + 11b2 + -7b2 = -4 + b + 7b2 + 4 + -1b + -7b2

Combine like terms: -1 + 4 = 3
3 + -12b + -1b + 11b2 + -7b2 = -4 + b + 7b2 + 4 + -1b + -7b2

Combine like terms: -12b + -1b = -13b
3 + -13b + 11b2 + -7b2 = -4 + b + 7b2 + 4 + -1b + -7b2

Combine like terms: 11b2 + -7b2 = 4b2
3 + -13b + 4b2 = -4 + b + 7b2 + 4 + -1b + -7b2

Reorder the terms:
3 + -13b + 4b2 = -4 + 4 + b + -1b + 7b2 + -7b2

Combine like terms: -4 + 4 = 0
3 + -13b + 4b2 = 0 + b + -1b + 7b2 + -7b2
3 + -13b + 4b2 = b + -1b + 7b2 + -7b2

Combine like terms: b + -1b = 0
3 + -13b + 4b2 = 0 + 7b2 + -7b2
3 + -13b + 4b2 = 7b2 + -7b2

Combine like terms: 7b2 + -7b2 = 0
3 + -13b + 4b2 = 0

Factor a trinomial.
(1 + -4b)(3 + -1b) = 0

Subproblem 1
Set the factor '(1 + -4b)' equal to zero and attempt to solve:

Simplifying
1 + -4b = 0

Solving
1 + -4b = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4b = 0 + -1
-4b = 0 + -1

Combine like terms: 0 + -1 = -1
-4b = -1

Divide each side by '-4'.
b = 0.25

Simplifying
b = 0.25
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {0.25, 3}