a(3a-11)=20

Solution for a(3a-11)=20 equation:

Simplifying
a(3a + -11) = 20

Reorder the terms:
a(-11 + 3a) = 20
(-11 * a + 3a * a) = 20
(-11a + 3a2) = 20

Solving
-11a + 3a2 = 20

Solving for variable 'a'.

Reorder the terms:
-20 + -11a + 3a2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -11a + 3a2 = 0

Factor a trinomial.
(-4 + -3a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve:

Simplifying
-4 + -3a = 0

Solving
-4 + -3a = 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 + -3a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3a = 0 + 4
-3a = 0 + 4

Combine like terms: 0 + 4 = 4
-3a = 4

Divide each side by '-3'.
a = -1.333333333

Simplifying
a = -1.333333333
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-1.333333333, 5}