81x^2+162x+75=0

Solution for 81x^2+162x+75=0 equation:

Simplifying
81x2 + 162x + 75 = 0

Reorder the terms:
75 + 162x + 81x2 = 0

Solving
75 + 162x + 81x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 54x + 27x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(25 + 54x + 27x2)' equal to zero and attempt to solve:

Simplifying
25 + 54x + 27x2 = 0

Solving
25 + 54x + 27x2 = 0

Begin completing the square.  Divide all terms by
27 the coefficient of the squared term: 

Divide each side by '27'.
0.9259259259 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.9259259259' to each side of the equation.
0.9259259259 + 2x + -0.9259259259 + x2 = 0 + -0.9259259259

Reorder the terms:
0.9259259259 + -0.9259259259 + 2x + x2 = 0 + -0.9259259259

Combine like terms: 0.9259259259 + -0.9259259259 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.9259259259
2x + x2 = 0 + -0.9259259259

Combine like terms: 0 + -0.9259259259 = -0.9259259259
2x + x2 = -0.9259259259

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.9259259259 + 1

Reorder the terms:
1 + 2x + x2 = -0.9259259259 + 1

Combine like terms: -0.9259259259 + 1 = 0.0740740741
1 + 2x + x2 = 0.0740740741

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.0740740741

Calculate the square root of the right side: 0.272165527

Break this problem into two subproblems by setting 
(x + 1) equal to 0.272165527 and -0.272165527.

Subproblem 1
x + 1 = 0.272165527

Simplifying
x + 1 = 0.272165527

Reorder the terms:
1 + x = 0.272165527

Solving
1 + x = 0.272165527

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.272165527 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.272165527 + -1
x = 0.272165527 + -1

Combine like terms: 0.272165527 + -1 = -0.727834473
x = -0.727834473

Simplifying
x = -0.727834473

Subproblem 2
x + 1 = -0.272165527

Simplifying
x + 1 = -0.272165527

Reorder the terms:
1 + x = -0.272165527

Solving
1 + x = -0.272165527

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.272165527 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.272165527 + -1
x = -0.272165527 + -1

Combine like terms: -0.272165527 + -1 = -1.272165527
x = -1.272165527

Simplifying
x = -1.272165527

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.727834473, -1.272165527}
Solution
x = {-0.727834473, -1.272165527}