6b^2=42b-72

Solution for 6b^2=42b-72 equation:

Simplifying
6b2 = 42b + -72

Reorder the terms:
6b2 = -72 + 42b

Solving
6b2 = -72 + 42b

Solving for variable 'b'.

Reorder the terms:
72 + -42b + 6b2 = -72 + 42b + 72 + -42b

Reorder the terms:
72 + -42b + 6b2 = -72 + 72 + 42b + -42b

Combine like terms: -72 + 72 = 0
72 + -42b + 6b2 = 0 + 42b + -42b
72 + -42b + 6b2 = 42b + -42b

Combine like terms: 42b + -42b = 0
72 + -42b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7b + b2) = 0

Factor a trinomial.
6((3 + -1b)(4 + -1b)) = 0

Ignore the factor 6.
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 '(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 = {3, 4}