b^2-4b=3b+30

Solution for b^2-4b=3b+30 equation:

Simplifying
b2 + -4b = 3b + 30

Reorder the terms:
-4b + b2 = 3b + 30

Reorder the terms:
-4b + b2 = 30 + 3b

Solving
-4b + b2 = 30 + 3b

Solving for variable 'b'.

Reorder the terms:
-30 + -4b + -3b + b2 = 30 + 3b + -30 + -3b

Combine like terms: -4b + -3b = -7b
-30 + -7b + b2 = 30 + 3b + -30 + -3b

Reorder the terms:
-30 + -7b + b2 = 30 + -30 + 3b + -3b

Combine like terms: 30 + -30 = 0
-30 + -7b + b2 = 0 + 3b + -3b
-30 + -7b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-30 + -7b + b2 = 0

Factor a trinomial.
(-3 + -1b)(10 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1b)' equal to zero and attempt to solve:

Simplifying
10 + -1b = 0

Solving
10 + -1b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1b = 0 + -10
-1b = 0 + -10

Combine like terms: 0 + -10 = -10
-1b = -10

Divide each side by '-1'.
b = 10

Simplifying
b = 10
Solution
b = {-3, 10}