75a^2+90a+27=

Solution for 75a^2+90a+27= equation:

Simplifying
75a2 + 90a + 27 = 0

Reorder the terms:
27 + 90a + 75a2 = 0

Solving
27 + 90a + 75a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 30a + 25a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5a = 0 + -3

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

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

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5a = 0 + -3

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

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

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Solution
a = {-0.6, -0.6}