(-4m+2)(-4m+2)-17=11

Solution for (-4m+2)(-4m+2)-17=11 equation:

Simplifying
(-4m + 2)(-4m + 2) + -17 = 11

Reorder the terms:
(2 + -4m)(-4m + 2) + -17 = 11

Reorder the terms:
(2 + -4m)(2 + -4m) + -17 = 11

Multiply (2 + -4m) * (2 + -4m)
(2(2 + -4m) + -4m * (2 + -4m)) + -17 = 11
((2 * 2 + -4m * 2) + -4m * (2 + -4m)) + -17 = 11
((4 + -8m) + -4m * (2 + -4m)) + -17 = 11
(4 + -8m + (2 * -4m + -4m * -4m)) + -17 = 11
(4 + -8m + (-8m + 16m2)) + -17 = 11

Combine like terms: -8m + -8m = -16m
(4 + -16m + 16m2) + -17 = 11

Reorder the terms:
4 + -17 + -16m + 16m2 = 11

Combine like terms: 4 + -17 = -13
-13 + -16m + 16m2 = 11

Solving
-13 + -16m + 16m2 = 11

Solving for variable 'm'.

Reorder the terms:
-13 + -11 + -16m + 16m2 = 11 + -11

Combine like terms: -13 + -11 = -24
-24 + -16m + 16m2 = 11 + -11

Combine like terms: 11 + -11 = 0
-24 + -16m + 16m2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + -2m + 2m2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -2m + 2m2)' equal to zero and attempt to solve:

Simplifying
-3 + -2m + 2m2 = 0

Solving
-3 + -2m + 2m2 = 0

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

Divide each side by '2'.
-1.5 + -1m + m2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1m + 1.5 + m2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1m + m2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1m + m2 = 0 + 1.5
-1m + m2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1m + m2 = 1.5

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 1.5 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + -1m + m2 = 1.75

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(m + -0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
m + -0.5 = 1.322875656

Simplifying
m + -0.5 = 1.322875656

Reorder the terms:
-0.5 + m = 1.322875656

Solving
-0.5 + m = 1.322875656

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 1.322875656 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 1.322875656 + 0.5
m = 1.322875656 + 0.5

Combine like terms: 1.322875656 + 0.5 = 1.822875656
m = 1.822875656

Simplifying
m = 1.822875656

Subproblem 2
m + -0.5 = -1.322875656

Simplifying
m + -0.5 = -1.322875656

Reorder the terms:
-0.5 + m = -1.322875656

Solving
-0.5 + m = -1.322875656

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -1.322875656 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -1.322875656 + 0.5
m = -1.322875656 + 0.5

Combine like terms: -1.322875656 + 0.5 = -0.822875656
m = -0.822875656

Simplifying
m = -0.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.822875656, -0.822875656}
Solution
m = {1.822875656, -0.822875656}