2b^2+12b=14

Solution for 2b^2+12b=14 equation:

Simplifying
2b2 + 12b = 14

Reorder the terms:
12b + 2b2 = 14

Solving
12b + 2b2 = 14

Solving for variable 'b'.

Reorder the terms:
-14 + 12b + 2b2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 12b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6b + b2) = 0

Factor a trinomial.
2((-7 + -1b)(1 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1b)' equal to zero and attempt to solve:

Simplifying
-7 + -1b = 0

Solving
-7 + -1b = 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 + -1b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1b = 0 + 7
-1b = 0 + 7

Combine like terms: 0 + 7 = 7
-1b = 7

Divide each side by '-1'.
b = -7

Simplifying
b = -7
Subproblem 2
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
Solution
b = {-7, 1}