4a^2=-5a

Solution for 4a^2=-5a equation:

Simplifying
4a2 = -5a

Solving
4a2 = -5a

Solving for variable 'a'.

Reorder the terms:
5a + 4a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
5a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(5 + 4a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(5 + 4a)' equal to zero and attempt to solve:

Simplifying
5 + 4a = 0

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

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

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

Divide each side by '4'.
a = -1.25

Simplifying
a = -1.25
Solution
a = {0, -1.25}