21b^2-60b+22=b-6

Solution for 21b^2-60b+22=b-6 equation:

Simplifying
21b2 + -60b + 22 = b + -6

Reorder the terms:
22 + -60b + 21b2 = b + -6

Reorder the terms:
22 + -60b + 21b2 = -6 + b

Solving
22 + -60b + 21b2 = -6 + b

Solving for variable 'b'.

Reorder the terms:
22 + 6 + -60b + -1b + 21b2 = -6 + b + 6 + -1b

Combine like terms: 22 + 6 = 28
28 + -60b + -1b + 21b2 = -6 + b + 6 + -1b

Combine like terms: -60b + -1b = -61b
28 + -61b + 21b2 = -6 + b + 6 + -1b

Reorder the terms:
28 + -61b + 21b2 = -6 + 6 + b + -1b

Combine like terms: -6 + 6 = 0
28 + -61b + 21b2 = 0 + b + -1b
28 + -61b + 21b2 = b + -1b

Combine like terms: b + -1b = 0
28 + -61b + 21b2 = 0

Factor a trinomial.
(4 + -7b)(7 + -3b) = 0

Subproblem 1
Set the factor '(4 + -7b)' equal to zero and attempt to solve:

Simplifying
4 + -7b = 0

Solving
4 + -7b = 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 + -7b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7b = 0 + -4
-7b = 0 + -4

Combine like terms: 0 + -4 = -4
-7b = -4

Divide each side by '-7'.
b = 0.5714285714

Simplifying
b = 0.5714285714
Subproblem 2
Set the factor '(7 + -3b)' equal to zero and attempt to solve:

Simplifying
7 + -3b = 0

Solving
7 + -3b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3b = 0 + -7

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

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

Divide each side by '-3'.
b = 2.333333333

Simplifying
b = 2.333333333
Solution
b = {0.5714285714, 2.333333333}