3q^2=5q+2

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

Simplifying
3q2 = 5q + 2

Reorder the terms:
3q2 = 2 + 5q

Solving
3q2 = 2 + 5q

Solving for variable 'q'.

Reorder the terms:
-2 + -5q + 3q2 = 2 + 5q + -2 + -5q

Reorder the terms:
-2 + -5q + 3q2 = 2 + -2 + 5q + -5q

Combine like terms: 2 + -2 = 0
-2 + -5q + 3q2 = 0 + 5q + -5q
-2 + -5q + 3q2 = 5q + -5q

Combine like terms: 5q + -5q = 0
-2 + -5q + 3q2 = 0

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

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

Simplifying
-1 + -3q = 0

Solving
-1 + -3q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3q = 0 + 1
-3q = 0 + 1

Combine like terms: 0 + 1 = 1
-3q = 1

Divide each side by '-3'.
q = -0.3333333333

Simplifying
q = -0.3333333333
Subproblem 2
Set the factor '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

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

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

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Solution
q = {-0.3333333333, 2}