75x^2+90x+27=0

Solution for 75x^2+90x+27=0 equation:

Simplifying
75x2 + 90x + 27 = 0

Reorder the terms:
27 + 90x + 75x2 = 0

Solving
27 + 90x + 75x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 30x + 25x2) = 0

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

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

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

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

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

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

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

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

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

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

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

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

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

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