2a^2=11a-12

Solution for 2a^2=11a-12 equation:

Simplifying
2a2 = 11a + -12

Reorder the terms:
2a2 = -12 + 11a

Solving
2a2 = -12 + 11a

Solving for variable 'a'.

Reorder the terms:
12 + -11a + 2a2 = -12 + 11a + 12 + -11a

Reorder the terms:
12 + -11a + 2a2 = -12 + 12 + 11a + -11a

Combine like terms: -12 + 12 = 0
12 + -11a + 2a2 = 0 + 11a + -11a
12 + -11a + 2a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
12 + -11a + 2a2 = 0

Factor a trinomial.
(3 + -2a)(4 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {1.5, 4}