2a(a+3)=3a(a+2)

Solution for 2a(a+3)=3a(a+2) equation:

Simplifying
2a(a + 3) = 3a(a + 2)

Reorder the terms:
2a(3 + a) = 3a(a + 2)
(3 * 2a + a * 2a) = 3a(a + 2)
(6a + 2a2) = 3a(a + 2)

Reorder the terms:
6a + 2a2 = 3a(2 + a)
6a + 2a2 = (2 * 3a + a * 3a)
6a + 2a2 = (6a + 3a2)

Add '-6a' to each side of the equation.
6a + -6a + 2a2 = 6a + -6a + 3a2

Combine like terms: 6a + -6a = 0
0 + 2a2 = 6a + -6a + 3a2
2a2 = 6a + -6a + 3a2

Combine like terms: 6a + -6a = 0
2a2 = 0 + 3a2
2a2 = 3a2

Solving
2a2 = 3a2

Solving for variable 'a'.

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

Add '-3a2' to each side of the equation.
2a2 + -3a2 = 3a2 + -3a2

Combine like terms: 2a2 + -3a2 = -1a2
-1a2 = 3a2 + -3a2

Combine like terms: 3a2 + -3a2 = 0
-1a2 = 0

Divide each side by '-1'.
a2 = 0

Simplifying
a2 = 0

Take the square root of each side:
a = {0}