5-2m(1+4m)=-13

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Solution for 5-2m(1+4m)=-13 equation: 


Simplifying
5 + -2m(1 + 4m) = -13
5 + (1 * -2m + 4m * -2m) = -13
5 + (-2m + -8m2) = -13

Solving
5 + -2m + -8m2 = -13

Solving for variable 'm'.

Reorder the terms:
5 + 13 + -2m + -8m2 = -13 + 13

Combine like terms: 5 + 13 = 18
18 + -2m + -8m2 = -13 + 13

Combine like terms: -13 + 13 = 0
18 + -2m + -8m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -1m + -4m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -1m + -4m2)' equal to zero and attempt to solve:

Simplifying
9 + -1m + -4m2 = 0

Solving
9 + -1m + -4m2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + 0.25m + m2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.25m + 2.25 + m2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.25m + m2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.25m + m2 = 0 + 2.25
0.25m + m2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.25m + m2 = 2.25

The m term is 0.25m.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25m + 0.015625 + m2 = 2.25 + 0.015625

Reorder the terms:
0.015625 + 0.25m + m2 = 2.25 + 0.015625

Combine like terms: 2.25 + 0.015625 = 2.265625
0.015625 + 0.25m + m2 = 2.265625

Factor a perfect square on the left side:
(m + 0.125)(m + 0.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(m + 0.125) equal to 1.505199322 and -1.505199322.


Subproblem 1
m + 0.125 = 1.505199322

Simplifying
m + 0.125 = 1.505199322

Reorder the terms:
0.125 + m = 1.505199322

Solving
0.125 + m = 1.505199322

Solving for variable 'm'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + m = 1.505199322 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + m = 1.505199322 + -0.125
m = 1.505199322 + -0.125

Combine like terms: 1.505199322 + -0.125 = 1.380199322
m = 1.380199322

Simplifying
m = 1.380199322


Subproblem 2
m + 0.125 = -1.505199322

Simplifying
m + 0.125 = -1.505199322

Reorder the terms:
0.125 + m = -1.505199322

Solving
0.125 + m = -1.505199322

Solving for variable 'm'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + m = -1.505199322 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + m = -1.505199322 + -0.125
m = -1.505199322 + -0.125

Combine like terms: -1.505199322 + -0.125 = -1.630199322
m = -1.630199322

Simplifying
m = -1.630199322


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.380199322, -1.630199322}
Solution
m = {1.380199322, -1.630199322}

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