10b^2-28b-6=0

Solution for 10b^2-28b-6=0 equation:

Simplifying
10b2 + -28b + -6 = 0

Reorder the terms:
-6 + -28b + 10b2 = 0

Solving
-6 + -28b + 10b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -14b + 5b2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5b)' equal to zero and attempt to solve:

Simplifying
-1 + -5b = 0

Solving
-1 + -5b = 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 + -5b = 0 + 1

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

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

Divide each side by '-5'.
b = -0.2

Simplifying
b = -0.2
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 = {-0.2, 3}