5b^2=3b+2

Solution for 5b^2=3b+2 equation:

Simplifying
5b2 = 3b + 2

Reorder the terms:
5b2 = 2 + 3b

Solving
5b2 = 2 + 3b

Solving for variable 'b'.

Reorder the terms:
-2 + -3b + 5b2 = 2 + 3b + -2 + -3b

Reorder the terms:
-2 + -3b + 5b2 = 2 + -2 + 3b + -3b

Combine like terms: 2 + -2 = 0
-2 + -3b + 5b2 = 0 + 3b + -3b
-2 + -3b + 5b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-2 + -3b + 5b2 = 0

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

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

Simplifying
-2 + -5b = 0

Solving
-2 + -5b = 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 + -5b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5b = 0 + 2
-5b = 0 + 2

Combine like terms: 0 + 2 = 2
-5b = 2

Divide each side by '-5'.
b = -0.4

Simplifying
b = -0.4
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

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

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

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

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

Simplifying
b = 1
Solution
b = {-0.4, 1}