36m^2-32m-36=

Solution for 36m^2-32m-36= equation:

Simplifying
36m2 + -32m + -36 = 0

Reorder the terms:
-36 + -32m + 36m2 = 0

Solving
-36 + -32m + 36m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -8m + 9m2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -8m + 9m2)' equal to zero and attempt to solve:

Simplifying
-9 + -8m + 9m2 = 0

Solving
-9 + -8m + 9m2 = 0

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

Divide each side by '9'.
-1 + -0.8888888889m + m2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.8888888889m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.8888888889m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.8888888889m + m2 = 0 + 1
-0.8888888889m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.8888888889m + m2 = 1

The m term is -0.8888888889m.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889m + 0.1975308642 + m2 = 1 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889m + m2 = 1 + 0.1975308642

Combine like terms: 1 + 0.1975308642 = 1.1975308642
0.1975308642 + -0.8888888889m + m2 = 1.1975308642

Factor a perfect square on the left side:
(m + -0.4444444445)(m + -0.4444444445) = 1.1975308642

Calculate the square root of the right side: 1.094317534

Break this problem into two subproblems by setting 
(m + -0.4444444445) equal to 1.094317534 and -1.094317534.

Subproblem 1
m + -0.4444444445 = 1.094317534

Simplifying
m + -0.4444444445 = 1.094317534

Reorder the terms:
-0.4444444445 + m = 1.094317534

Solving
-0.4444444445 + m = 1.094317534

Solving for variable 'm'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + m = 1.094317534 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + m = 1.094317534 + 0.4444444445
m = 1.094317534 + 0.4444444445

Combine like terms: 1.094317534 + 0.4444444445 = 1.5387619785
m = 1.5387619785

Simplifying
m = 1.5387619785

Subproblem 2
m + -0.4444444445 = -1.094317534

Simplifying
m + -0.4444444445 = -1.094317534

Reorder the terms:
-0.4444444445 + m = -1.094317534

Solving
-0.4444444445 + m = -1.094317534

Solving for variable 'm'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + m = -1.094317534 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + m = -1.094317534 + 0.4444444445
m = -1.094317534 + 0.4444444445

Combine like terms: -1.094317534 + 0.4444444445 = -0.6498730895
m = -0.6498730895

Simplifying
m = -0.6498730895

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.5387619785, -0.6498730895}
Solution
m = {1.5387619785, -0.6498730895}