2b^2=13b+7

Solution for 2b^2=13b+7 equation:

Simplifying
2b2 = 13b + 7

Reorder the terms:
2b2 = 7 + 13b

Solving
2b2 = 7 + 13b

Solving for variable 'b'.

Reorder the terms:
-7 + -13b + 2b2 = 7 + 13b + -7 + -13b

Reorder the terms:
-7 + -13b + 2b2 = 7 + -7 + 13b + -13b

Combine like terms: 7 + -7 = 0
-7 + -13b + 2b2 = 0 + 13b + -13b
-7 + -13b + 2b2 = 13b + -13b

Combine like terms: 13b + -13b = 0
-7 + -13b + 2b2 = 0

Factor a trinomial.
(-1 + -2b)(7 + -1b) = 0

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

Simplifying
-1 + -2b = 0

Solving
-1 + -2b = 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 + -2b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2b = 0 + 1
-2b = 0 + 1

Combine like terms: 0 + 1 = 1
-2b = 1

Divide each side by '-2'.
b = -0.5

Simplifying
b = -0.5
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-0.5, 7}