6m^2-48m+18=0

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Solution for 6m^2-48m+18=0 equation: 


Simplifying
6m2 + -48m + 18 = 0

Reorder the terms:
18 + -48m + 6m2 = 0

Solving
18 + -48m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -8m + m2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(3 + -8m + m2)' equal to zero and attempt to solve:

Simplifying
3 + -8m + m2 = 0

Solving
3 + -8m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8m + -3 + m2 = 0 + -3

Reorder the terms:
3 + -3 + -8m + m2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8m + m2 = 0 + -3
-8m + m2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8m + m2 = -3

The m term is -8m.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8m + 16 + m2 = -3 + 16

Reorder the terms:
16 + -8m + m2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8m + m2 = 13

Factor a perfect square on the left side:
(m + -4)(m + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(m + -4) equal to 3.605551275 and -3.605551275.


Subproblem 1
m + -4 = 3.605551275

Simplifying
m + -4 = 3.605551275

Reorder the terms:
-4 + m = 3.605551275

Solving
-4 + m = 3.605551275

Solving for variable 'm'.

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

Add '4' to each side of the equation.
-4 + 4 + m = 3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + m = 3.605551275 + 4
m = 3.605551275 + 4

Combine like terms: 3.605551275 + 4 = 7.605551275
m = 7.605551275

Simplifying
m = 7.605551275


Subproblem 2
m + -4 = -3.605551275

Simplifying
m + -4 = -3.605551275

Reorder the terms:
-4 + m = -3.605551275

Solving
-4 + m = -3.605551275

Solving for variable 'm'.

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

Add '4' to each side of the equation.
-4 + 4 + m = -3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + m = -3.605551275 + 4
m = -3.605551275 + 4

Combine like terms: -3.605551275 + 4 = 0.394448725
m = 0.394448725

Simplifying
m = 0.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.605551275, 0.394448725}
Solution
m = {7.605551275, 0.394448725}

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