-16m^2-12m+36=0

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Solution for -16m^2-12m+36=0 equation: 


Simplifying
-16m2 + -12m + 36 = 0

Reorder the terms:
36 + -12m + -16m2 = 0

Solving
36 + -12m + -16m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -3m + -4m2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + -3m + -4m2)' equal to zero and attempt to solve:

Simplifying
9 + -3m + -4m2 = 0

Solving
9 + -3m + -4m2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + 0.75m + m2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.75m + 2.25 + m2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.75m + m2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.75m + m2 = 0 + 2.25
0.75m + m2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.75m + m2 = 2.25

The m term is 0.75m.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75m + 0.140625 + m2 = 2.25 + 0.140625

Reorder the terms:
0.140625 + 0.75m + m2 = 2.25 + 0.140625

Combine like terms: 2.25 + 0.140625 = 2.390625
0.140625 + 0.75m + m2 = 2.390625

Factor a perfect square on the left side:
(m + 0.375)(m + 0.375) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(m + 0.375) equal to 1.54616461 and -1.54616461.


Subproblem 1
m + 0.375 = 1.54616461

Simplifying
m + 0.375 = 1.54616461

Reorder the terms:
0.375 + m = 1.54616461

Solving
0.375 + m = 1.54616461

Solving for variable 'm'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + m = 1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + m = 1.54616461 + -0.375
m = 1.54616461 + -0.375

Combine like terms: 1.54616461 + -0.375 = 1.17116461
m = 1.17116461

Simplifying
m = 1.17116461


Subproblem 2
m + 0.375 = -1.54616461

Simplifying
m + 0.375 = -1.54616461

Reorder the terms:
0.375 + m = -1.54616461

Solving
0.375 + m = -1.54616461

Solving for variable 'm'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + m = -1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + m = -1.54616461 + -0.375
m = -1.54616461 + -0.375

Combine like terms: -1.54616461 + -0.375 = -1.92116461
m = -1.92116461

Simplifying
m = -1.92116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.17116461, -1.92116461}
Solution
m = {1.17116461, -1.92116461}

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