3(2m+5)(2m+5)=23

Solution for 3(2m+5)(2m+5)=23 equation:

Simplifying
3(2m + 5)(2m + 5) = 23

Reorder the terms:
3(5 + 2m)(2m + 5) = 23

Reorder the terms:
3(5 + 2m)(5 + 2m) = 23

Multiply (5 + 2m) * (5 + 2m)
3(5(5 + 2m) + 2m * (5 + 2m)) = 23
3((5 * 5 + 2m * 5) + 2m * (5 + 2m)) = 23
3((25 + 10m) + 2m * (5 + 2m)) = 23
3(25 + 10m + (5 * 2m + 2m * 2m)) = 23
3(25 + 10m + (10m + 4m2)) = 23

Combine like terms: 10m + 10m = 20m
3(25 + 20m + 4m2) = 23
(25 * 3 + 20m * 3 + 4m2 * 3) = 23
(75 + 60m + 12m2) = 23

Solving
75 + 60m + 12m2 = 23

Solving for variable 'm'.

Reorder the terms:
75 + -23 + 60m + 12m2 = 23 + -23

Combine like terms: 75 + -23 = 52
52 + 60m + 12m2 = 23 + -23

Combine like terms: 23 + -23 = 0
52 + 60m + 12m2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + 15m + 3m2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(13 + 15m + 3m2)' equal to zero and attempt to solve:

Simplifying
13 + 15m + 3m2 = 0

Solving
13 + 15m + 3m2 = 0

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

Divide each side by '3'.
4.333333333 + 5m + m2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 5m + -4.333333333 + m2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 5m + m2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 5m + m2 = 0 + -4.333333333
5m + m2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
5m + m2 = -4.333333333

The m term is 5m.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m + 6.25 + m2 = -4.333333333 + 6.25

Reorder the terms:
6.25 + 5m + m2 = -4.333333333 + 6.25

Combine like terms: -4.333333333 + 6.25 = 1.916666667
6.25 + 5m + m2 = 1.916666667

Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(m + 2.5) equal to 1.384437311 and -1.384437311.

Subproblem 1
m + 2.5 = 1.384437311

Simplifying
m + 2.5 = 1.384437311

Reorder the terms:
2.5 + m = 1.384437311

Solving
2.5 + m = 1.384437311

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = 1.384437311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = 1.384437311 + -2.5
m = 1.384437311 + -2.5

Combine like terms: 1.384437311 + -2.5 = -1.115562689
m = -1.115562689

Simplifying
m = -1.115562689

Subproblem 2
m + 2.5 = -1.384437311

Simplifying
m + 2.5 = -1.384437311

Reorder the terms:
2.5 + m = -1.384437311

Solving
2.5 + m = -1.384437311

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = -1.384437311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = -1.384437311 + -2.5
m = -1.384437311 + -2.5

Combine like terms: -1.384437311 + -2.5 = -3.884437311
m = -3.884437311

Simplifying
m = -3.884437311

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.115562689, -3.884437311}
Solution
m = {-1.115562689, -3.884437311}