2a^2+ab=3b^2

Solution for 2a^2+ab=3b^2 equation:

Simplifying
2a2 + ab = 3b2

Reorder the terms:
ab + 2a2 = 3b2

Solving
ab + 2a2 = 3b2

Solving for variable 'a'.

Combine like terms: 3b2 + -3b2 = 0
ab + 2a2 + -3b2 = 0

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

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Subproblem 2
Set the factor '(2a + 3b)' equal to zero and attempt to solve:

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

Add '-3b' to each side of the equation.
2a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
2a + 0 = 0 + -3b
2a = 0 + -3b
Remove the zero:
2a = -3b

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Solution
a = {b, -1.5b}