2b^2+5b=3

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

Simplifying
2b2 + 5b = 3

Reorder the terms:
5b + 2b2 = 3

Solving
5b + 2b2 = 3

Solving for variable 'b'.

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

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

Factor a trinomial.
(-3 + -1b)(1 + -2b) = 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 '(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
Solution
b = {-3, 0.5}