12m^2-96=12m+3m

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Solution for 12m^2-96=12m+3m equation: 


Simplifying
12m2 + -96 = 12m + 3m

Reorder the terms:
-96 + 12m2 = 12m + 3m

Combine like terms: 12m + 3m = 15m
-96 + 12m2 = 15m

Solving
-96 + 12m2 = 15m

Solving for variable 'm'.

Reorder the terms:
-96 + -15m + 12m2 = 15m + -15m

Combine like terms: 15m + -15m = 0
-96 + -15m + 12m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + -5m + 4m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-32 + -5m + 4m2)' equal to zero and attempt to solve:

Simplifying
-32 + -5m + 4m2 = 0

Solving
-32 + -5m + 4m2 = 0

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

Divide each side by '4'.
-8 + -1.25m + m2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1.25m + 8 + m2 = 0 + 8

Reorder the terms:
-8 + 8 + -1.25m + m2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1.25m + m2 = 0 + 8
-1.25m + m2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1.25m + m2 = 8

The m term is -1.25m.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25m + 0.390625 + m2 = 8 + 0.390625

Reorder the terms:
0.390625 + -1.25m + m2 = 8 + 0.390625

Combine like terms: 8 + 0.390625 = 8.390625
0.390625 + -1.25m + m2 = 8.390625

Factor a perfect square on the left side:
(m + -0.625)(m + -0.625) = 8.390625

Calculate the square root of the right side: 2.896657557

Break this problem into two subproblems by setting 
(m + -0.625) equal to 2.896657557 and -2.896657557.


Subproblem 1
m + -0.625 = 2.896657557

Simplifying
m + -0.625 = 2.896657557

Reorder the terms:
-0.625 + m = 2.896657557

Solving
-0.625 + m = 2.896657557

Solving for variable 'm'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + m = 2.896657557 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = 2.896657557 + 0.625
m = 2.896657557 + 0.625

Combine like terms: 2.896657557 + 0.625 = 3.521657557
m = 3.521657557

Simplifying
m = 3.521657557


Subproblem 2
m + -0.625 = -2.896657557

Simplifying
m + -0.625 = -2.896657557

Reorder the terms:
-0.625 + m = -2.896657557

Solving
-0.625 + m = -2.896657557

Solving for variable 'm'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + m = -2.896657557 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = -2.896657557 + 0.625
m = -2.896657557 + 0.625

Combine like terms: -2.896657557 + 0.625 = -2.271657557
m = -2.271657557

Simplifying
m = -2.271657557


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.521657557, -2.271657557}
Solution
m = {3.521657557, -2.271657557}

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