b^2+13b+25=6b+43

Solution for b^2+13b+25=6b+43 equation:

Simplifying
b2 + 13b + 25 = 6b + 43

Reorder the terms:
25 + 13b + b2 = 6b + 43

Reorder the terms:
25 + 13b + b2 = 43 + 6b

Solving
25 + 13b + b2 = 43 + 6b

Solving for variable 'b'.

Reorder the terms:
25 + -43 + 13b + -6b + b2 = 43 + 6b + -43 + -6b

Combine like terms: 25 + -43 = -18
-18 + 13b + -6b + b2 = 43 + 6b + -43 + -6b

Combine like terms: 13b + -6b = 7b
-18 + 7b + b2 = 43 + 6b + -43 + -6b

Reorder the terms:
-18 + 7b + b2 = 43 + -43 + 6b + -6b

Combine like terms: 43 + -43 = 0
-18 + 7b + b2 = 0 + 6b + -6b
-18 + 7b + b2 = 6b + -6b

Combine like terms: 6b + -6b = 0
-18 + 7b + b2 = 0

Factor a trinomial.
(-9 + -1b)(2 + -1b) = 0

Subproblem 1
Set the factor '(-9 + -1b)' equal to zero and attempt to solve:

Simplifying
-9 + -1b = 0

Solving
-9 + -1b = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1b = 0 + 9
-1b = 0 + 9

Combine like terms: 0 + 9 = 9
-1b = 9

Divide each side by '-1'.
b = -9

Simplifying
b = -9
Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-9, 2}