5b^2+b-72=12

Solution for 5b^2+b-72=12 equation:

Simplifying
5b2 + b + -72 = 12

Reorder the terms:
-72 + b + 5b2 = 12

Solving
-72 + b + 5b2 = 12

Solving for variable 'b'.

Reorder the terms:
-72 + -12 + b + 5b2 = 12 + -12

Combine like terms: -72 + -12 = -84
-84 + b + 5b2 = 12 + -12

Combine like terms: 12 + -12 = 0
-84 + b + 5b2 = 0

Factor a trinomial.
(-21 + -5b)(4 + -1b) = 0

Subproblem 1
Set the factor '(-21 + -5b)' equal to zero and attempt to solve:

Simplifying
-21 + -5b = 0

Solving
-21 + -5b = 0

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

Add '21' to each side of the equation.
-21 + 21 + -5b = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -5b = 0 + 21
-5b = 0 + 21

Combine like terms: 0 + 21 = 21
-5b = 21

Divide each side by '-5'.
b = -4.2

Simplifying
b = -4.2
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

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

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

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

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-4.2, 4}