16a^2-24a+9+11a=a^2-4+33

Solution for 16a^2-24a+9+11a=a^2-4+33 equation:

Simplifying
16a2 + -24a + 9 + 11a = a2 + -4 + 33

Reorder the terms:
9 + -24a + 11a + 16a2 = a2 + -4 + 33

Combine like terms: -24a + 11a = -13a
9 + -13a + 16a2 = a2 + -4 + 33

Reorder the terms:
9 + -13a + 16a2 = -4 + 33 + a2

Combine like terms: -4 + 33 = 29
9 + -13a + 16a2 = 29 + a2

Solving
9 + -13a + 16a2 = 29 + a2

Solving for variable 'a'.

Reorder the terms:
9 + -29 + -13a + 16a2 + -1a2 = 29 + a2 + -29 + -1a2

Combine like terms: 9 + -29 = -20
-20 + -13a + 16a2 + -1a2 = 29 + a2 + -29 + -1a2

Combine like terms: 16a2 + -1a2 = 15a2
-20 + -13a + 15a2 = 29 + a2 + -29 + -1a2

Reorder the terms:
-20 + -13a + 15a2 = 29 + -29 + a2 + -1a2

Combine like terms: 29 + -29 = 0
-20 + -13a + 15a2 = 0 + a2 + -1a2
-20 + -13a + 15a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-20 + -13a + 15a2 = 0

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

Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + -5a = 0

Solving
-4 + -5a = 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 + -5a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5a = 0 + 4
-5a = 0 + 4

Combine like terms: 0 + 4 = 4
-5a = 4

Divide each side by '-5'.
a = -0.8

Simplifying
a = -0.8
Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-0.8, 1.666666667}