6b^2-7b-3=0

Solution for 6b^2-7b-3=0 equation:

Simplifying
6b2 + -7b + -3 = 0

Reorder the terms:
-3 + -7b + 6b2 = 0

Solving
-3 + -7b + 6b2 = 0

Solving for variable 'b'.

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

Subproblem 1
Set the factor '(-1 + -3b)' equal to zero and attempt to solve:

Simplifying
-1 + -3b = 0

Solving
-1 + -3b = 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 + -3b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3b = 0 + 1
-3b = 0 + 1

Combine like terms: 0 + 1 = 1
-3b = 1

Divide each side by '-3'.
b = -0.3333333333

Simplifying
b = -0.3333333333
Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2b = 0 + -3
-2b = 0 + -3

Combine like terms: 0 + -3 = -3
-2b = -3

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
Solution
b = {-0.3333333333, 1.5}