5a^2=-16+24a

Solution for 5a^2=-16+24a equation:

Simplifying
5a2 = -16 + 24a

Solving
5a2 = -16 + 24a

Solving for variable 'a'.

Reorder the terms:
16 + -24a + 5a2 = -16 + 24a + 16 + -24a

Reorder the terms:
16 + -24a + 5a2 = -16 + 16 + 24a + -24a

Combine like terms: -16 + 16 = 0
16 + -24a + 5a2 = 0 + 24a + -24a
16 + -24a + 5a2 = 24a + -24a

Combine like terms: 24a + -24a = 0
16 + -24a + 5a2 = 0

Factor a trinomial.
(4 + -5a)(4 + -1a) = 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 '(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 = {0.8, 4}