3b^2+7b=6

Solution for 3b^2+7b=6 equation:

Simplifying
3b2 + 7b = 6

Reorder the terms:
7b + 3b2 = 6

Solving
7b + 3b2 = 6

Solving for variable 'b'.

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

Combine like terms: 6 + -6 = 0
-6 + 7b + 3b2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve:

Simplifying
2 + -3b = 0

Solving
2 + -3b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3b = 0 + -2

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

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

Divide each side by '-3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Solution
b = {-3, 0.6666666667}