-7b^2+8b-69=-9-11b^2

Solution for -7b^2+8b-69=-9-11b^2 equation:

Simplifying
-7b2 + 8b + -69 = -9 + -11b2

Reorder the terms:
-69 + 8b + -7b2 = -9 + -11b2

Solving
-69 + 8b + -7b2 = -9 + -11b2

Solving for variable 'b'.

Reorder the terms:
-69 + 9 + 8b + -7b2 + 11b2 = -9 + -11b2 + 9 + 11b2

Combine like terms: -69 + 9 = -60
-60 + 8b + -7b2 + 11b2 = -9 + -11b2 + 9 + 11b2

Combine like terms: -7b2 + 11b2 = 4b2
-60 + 8b + 4b2 = -9 + -11b2 + 9 + 11b2

Reorder the terms:
-60 + 8b + 4b2 = -9 + 9 + -11b2 + 11b2

Combine like terms: -9 + 9 = 0
-60 + 8b + 4b2 = 0 + -11b2 + 11b2
-60 + 8b + 4b2 = -11b2 + 11b2

Combine like terms: -11b2 + 11b2 = 0
-60 + 8b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 2b + b2) = 0

Factor a trinomial.
4((-5 + -1b)(3 + -1b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve:

Simplifying
-5 + -1b = 0

Solving
-5 + -1b = 0

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

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

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

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

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

Simplifying
b = -5
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 = {-5, 3}