3(m-2)(m-2)=15

Solution for 3(m-2)(m-2)=15 equation:

Simplifying
3(m + -2)(m + -2) = 15

Reorder the terms:
3(-2 + m)(m + -2) = 15

Reorder the terms:
3(-2 + m)(-2 + m) = 15

Multiply (-2 + m) * (-2 + m)
3(-2(-2 + m) + m(-2 + m)) = 15
3((-2 * -2 + m * -2) + m(-2 + m)) = 15
3((4 + -2m) + m(-2 + m)) = 15
3(4 + -2m + (-2 * m + m * m)) = 15
3(4 + -2m + (-2m + m2)) = 15

Combine like terms: -2m + -2m = -4m
3(4 + -4m + m2) = 15
(4 * 3 + -4m * 3 + m2 * 3) = 15
(12 + -12m + 3m2) = 15

Solving
12 + -12m + 3m2 = 15

Solving for variable 'm'.

Reorder the terms:
12 + -15 + -12m + 3m2 = 15 + -15

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

Combine like terms: 15 + -15 = 0
-3 + -12m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -4m + m2) = 0

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

Simplifying
-1 + -4m + m2 = 0

Solving
-1 + -4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -4m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4m + m2 = 0 + 1
-4m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4m + m2 = 1

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 1 + 4

Reorder the terms:
4 + -4m + m2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4m + m2 = 5

Factor a perfect square on the left side:
(m + -2)(m + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(m + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
m + -2 = 2.236067978

Simplifying
m + -2 = 2.236067978

Reorder the terms:
-2 + m = 2.236067978

Solving
-2 + m = 2.236067978

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + m = 2.236067978 + 2
m = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
m = 4.236067978

Simplifying
m = 4.236067978

Subproblem 2
m + -2 = -2.236067978

Simplifying
m + -2 = -2.236067978

Reorder the terms:
-2 + m = -2.236067978

Solving
-2 + m = -2.236067978

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + m = -2.236067978 + 2
m = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
m = -0.236067978

Simplifying
m = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.236067978, -0.236067978}
Solution
m = {4.236067978, -0.236067978}