3b^2-13b=10

Solution for 3b^2-13b=10 equation:

Simplifying
3b2 + -13b = 10

Reorder the terms:
-13b + 3b2 = 10

Solving
-13b + 3b2 = 10

Solving for variable 'b'.

Reorder the terms:
-10 + -13b + 3b2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -13b + 3b2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
b = {-0.6666666667, 5}