2a^2-3a=18-12a

Solution for 2a^2-3a=18-12a equation:

Simplifying
2a2 + -3a = 18 + -12a

Reorder the terms:
-3a + 2a2 = 18 + -12a

Solving
-3a + 2a2 = 18 + -12a

Solving for variable 'a'.

Reorder the terms:
-18 + -3a + 12a + 2a2 = 18 + -12a + -18 + 12a

Combine like terms: -3a + 12a = 9a
-18 + 9a + 2a2 = 18 + -12a + -18 + 12a

Reorder the terms:
-18 + 9a + 2a2 = 18 + -18 + -12a + 12a

Combine like terms: 18 + -18 = 0
-18 + 9a + 2a2 = 0 + -12a + 12a
-18 + 9a + 2a2 = -12a + 12a

Combine like terms: -12a + 12a = 0
-18 + 9a + 2a2 = 0

Factor a trinomial.
(-6 + -1a)(3 + -2a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 0

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

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

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

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

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

Simplifying
a = 1.5
Solution
a = {-6, 1.5}