6b^2+12b-97=-7

Solution for 6b^2+12b-97=-7 equation:

Simplifying
6b2 + 12b + -97 = -7

Reorder the terms:
-97 + 12b + 6b2 = -7

Solving
-97 + 12b + 6b2 = -7

Solving for variable 'b'.

Reorder the terms:
-97 + 7 + 12b + 6b2 = -7 + 7

Combine like terms: -97 + 7 = -90
-90 + 12b + 6b2 = -7 + 7

Combine like terms: -7 + 7 = 0
-90 + 12b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 2b + b2) = 0

Factor a trinomial.
6((-5 + -1b)(3 + -1b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve:

Simplifying
-5 + -1b = 0

Solving
-5 + -1b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1b = 0 + 5
-1b = 0 + 5

Combine like terms: 0 + 5 = 5
-1b = 5

Divide each side by '-1'.
b = -5

Simplifying
b = -5
Subproblem 2
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
Solution
b = {-5, 3}