6b^2+2b=140

Solution for 6b^2+2b=140 equation:

Simplifying
6b2 + 2b = 140

Reorder the terms:
2b + 6b2 = 140

Solving
2b + 6b2 = 140

Solving for variable 'b'.

Reorder the terms:
-140 + 2b + 6b2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 2b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + b + 3b2) = 0

Factor a trinomial.
2((-5 + -1b)(14 + -3b)) = 0

Ignore the factor 2.
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 '(14 + -3b)' equal to zero and attempt to solve:

Simplifying
14 + -3b = 0

Solving
14 + -3b = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3b = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3b = 0 + -14
-3b = 0 + -14

Combine like terms: 0 + -14 = -14
-3b = -14

Divide each side by '-3'.
b = 4.666666667

Simplifying
b = 4.666666667
Solution
b = {-5, 4.666666667}