4=a(3a+11)

Solution for 4=a(3a+11) equation:

Simplifying
4 = a(3a + 11)

Reorder the terms:
4 = a(11 + 3a)
4 = (11 * a + 3a * a)
4 = (11a + 3a2)

Solving
4 = 11a + 3a2

Solving for variable 'a'.

Reorder the terms:
4 + -11a + -3a2 = 11a + -11a + 3a2 + -3a2

Combine like terms: 11a + -11a = 0
4 + -11a + -3a2 = 0 + 3a2 + -3a2
4 + -11a + -3a2 = 3a2 + -3a2

Combine like terms: 3a2 + -3a2 = 0
4 + -11a + -3a2 = 0

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

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

Simplifying
1 + -3a = 0

Solving
1 + -3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3a = 0 + -1

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

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

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

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

Simplifying
a = -4
Solution
a = {0.3333333333, -4}