2b^2=10b+12

Solution for 2b^2=10b+12 equation:

Simplifying
2b2 = 10b + 12

Reorder the terms:
2b2 = 12 + 10b

Solving
2b2 = 12 + 10b

Solving for variable 'b'.

Reorder the terms:
-12 + -10b + 2b2 = 12 + 10b + -12 + -10b

Reorder the terms:
-12 + -10b + 2b2 = 12 + -12 + 10b + -10b

Combine like terms: 12 + -12 = 0
-12 + -10b + 2b2 = 0 + 10b + -10b
-12 + -10b + 2b2 = 10b + -10b

Combine like terms: 10b + -10b = 0
-12 + -10b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5b + b2) = 0

Factor a trinomial.
2((-1 + -1b)(6 + -1b)) = 0

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 0

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

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

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

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-1, 6}