(4m-1)(25m+6)-(8m+1)=(6m-1)(6m+1)-11m

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Solution for (4m-1)(25m+6)-(8m+1)=(6m-1)(6m+1)-11m equation: 


Simplifying
(4m + -1)(25m + 6) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m

Reorder the terms:
(-1 + 4m)(25m + 6) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m

Reorder the terms:
(-1 + 4m)(6 + 25m) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m

Multiply (-1 + 4m) * (6 + 25m)
(-1(6 + 25m) + 4m * (6 + 25m)) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m
((6 * -1 + 25m * -1) + 4m * (6 + 25m)) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m
((-6 + -25m) + 4m * (6 + 25m)) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m
(-6 + -25m + (6 * 4m + 25m * 4m)) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m
(-6 + -25m + (24m + 100m2)) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m

Combine like terms: -25m + 24m = -1m
(-6 + -1m + 100m2) + -1(8m + 1) = (6m + -1)(6m + 1) + -11m

Reorder the terms:
-6 + -1m + 100m2 + -1(1 + 8m) = (6m + -1)(6m + 1) + -11m
-6 + -1m + 100m2 + (1 * -1 + 8m * -1) = (6m + -1)(6m + 1) + -11m
-6 + -1m + 100m2 + (-1 + -8m) = (6m + -1)(6m + 1) + -11m

Reorder the terms:
-6 + -1 + -1m + -8m + 100m2 = (6m + -1)(6m + 1) + -11m

Combine like terms: -6 + -1 = -7
-7 + -1m + -8m + 100m2 = (6m + -1)(6m + 1) + -11m

Combine like terms: -1m + -8m = -9m
-7 + -9m + 100m2 = (6m + -1)(6m + 1) + -11m

Reorder the terms:
-7 + -9m + 100m2 = (-1 + 6m)(6m + 1) + -11m

Reorder the terms:
-7 + -9m + 100m2 = (-1 + 6m)(1 + 6m) + -11m

Multiply (-1 + 6m) * (1 + 6m)
-7 + -9m + 100m2 = (-1(1 + 6m) + 6m * (1 + 6m)) + -11m
-7 + -9m + 100m2 = ((1 * -1 + 6m * -1) + 6m * (1 + 6m)) + -11m
-7 + -9m + 100m2 = ((-1 + -6m) + 6m * (1 + 6m)) + -11m
-7 + -9m + 100m2 = (-1 + -6m + (1 * 6m + 6m * 6m)) + -11m
-7 + -9m + 100m2 = (-1 + -6m + (6m + 36m2)) + -11m

Combine like terms: -6m + 6m = 0
-7 + -9m + 100m2 = (-1 + 0 + 36m2) + -11m
-7 + -9m + 100m2 = (-1 + 36m2) + -11m

Reorder the terms:
-7 + -9m + 100m2 = -1 + -11m + 36m2

Solving
-7 + -9m + 100m2 = -1 + -11m + 36m2

Solving for variable 'm'.

Reorder the terms:
-7 + 1 + -9m + 11m + 100m2 + -36m2 = -1 + -11m + 36m2 + 1 + 11m + -36m2

Combine like terms: -7 + 1 = -6
-6 + -9m + 11m + 100m2 + -36m2 = -1 + -11m + 36m2 + 1 + 11m + -36m2

Combine like terms: -9m + 11m = 2m
-6 + 2m + 100m2 + -36m2 = -1 + -11m + 36m2 + 1 + 11m + -36m2

Combine like terms: 100m2 + -36m2 = 64m2
-6 + 2m + 64m2 = -1 + -11m + 36m2 + 1 + 11m + -36m2

Reorder the terms:
-6 + 2m + 64m2 = -1 + 1 + -11m + 11m + 36m2 + -36m2

Combine like terms: -1 + 1 = 0
-6 + 2m + 64m2 = 0 + -11m + 11m + 36m2 + -36m2
-6 + 2m + 64m2 = -11m + 11m + 36m2 + -36m2

Combine like terms: -11m + 11m = 0
-6 + 2m + 64m2 = 0 + 36m2 + -36m2
-6 + 2m + 64m2 = 36m2 + -36m2

Combine like terms: 36m2 + -36m2 = 0
-6 + 2m + 64m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + m + 32m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + m + 32m2)' equal to zero and attempt to solve:

Simplifying
-3 + m + 32m2 = 0

Solving
-3 + m + 32m2 = 0

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

Divide each side by '32'.
-0.09375 + 0.03125m + m2 = 0

Move the constant term to the right:

Add '0.09375' to each side of the equation.
-0.09375 + 0.03125m + 0.09375 + m2 = 0 + 0.09375

Reorder the terms:
-0.09375 + 0.09375 + 0.03125m + m2 = 0 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + 0.03125m + m2 = 0 + 0.09375
0.03125m + m2 = 0 + 0.09375

Combine like terms: 0 + 0.09375 = 0.09375
0.03125m + m2 = 0.09375

The m term is m.  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.
0.03125m + 0.25 + m2 = 0.09375 + 0.25

Reorder the terms:
0.25 + 0.03125m + m2 = 0.09375 + 0.25

Combine like terms: 0.09375 + 0.25 = 0.34375
0.25 + 0.03125m + m2 = 0.34375

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.34375

Calculate the square root of the right side: 0.58630197

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.58630197 and -0.58630197.


Subproblem 1
m + 0.5 = 0.58630197

Simplifying
m + 0.5 = 0.58630197

Reorder the terms:
0.5 + m = 0.58630197

Solving
0.5 + m = 0.58630197

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 = 0.58630197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0.58630197 + -0.5
m = 0.58630197 + -0.5

Combine like terms: 0.58630197 + -0.5 = 0.08630197
m = 0.08630197

Simplifying
m = 0.08630197


Subproblem 2
m + 0.5 = -0.58630197

Simplifying
m + 0.5 = -0.58630197

Reorder the terms:
0.5 + m = -0.58630197

Solving
0.5 + m = -0.58630197

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 = -0.58630197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -0.58630197 + -0.5
m = -0.58630197 + -0.5

Combine like terms: -0.58630197 + -0.5 = -1.08630197
m = -1.08630197

Simplifying
m = -1.08630197


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.08630197, -1.08630197}
Solution
m = {0.08630197, -1.08630197}

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