4x(-4x-20)=5

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Solution for 4x(-4x-20)=5 equation: 


Simplifying
4x(-4x + -20) = 5

Reorder the terms:
4x(-20 + -4x) = 5
(-20 * 4x + -4x * 4x) = 5
(-80x + -16x2) = 5

Solving
-80x + -16x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -80x + -16x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -80x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 80x + 16x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 80x + 16x2)' equal to zero and attempt to solve:

Simplifying
5 + 80x + 16x2 = 0

Solving
5 + 80x + 16x2 = 0

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

Divide each side by '16'.
0.3125 + 5x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 5x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 5x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 5x + x2 = 0 + -0.3125
5x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
5x + x2 = -0.3125

The x term is 5x.  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.
5x + 6.25 + x2 = -0.3125 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -0.3125 + 6.25

Combine like terms: -0.3125 + 6.25 = 5.9375
6.25 + 5x + x2 = 5.9375

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.9375

Calculate the square root of the right side: 2.436698586

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.436698586 and -2.436698586.


Subproblem 1
x + 2.5 = 2.436698586

Simplifying
x + 2.5 = 2.436698586

Reorder the terms:
2.5 + x = 2.436698586

Solving
2.5 + x = 2.436698586

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.436698586 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.436698586 + -2.5
x = 2.436698586 + -2.5

Combine like terms: 2.436698586 + -2.5 = -0.063301414
x = -0.063301414

Simplifying
x = -0.063301414


Subproblem 2
x + 2.5 = -2.436698586

Simplifying
x + 2.5 = -2.436698586

Reorder the terms:
2.5 + x = -2.436698586

Solving
2.5 + x = -2.436698586

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.436698586 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.436698586 + -2.5
x = -2.436698586 + -2.5

Combine like terms: -2.436698586 + -2.5 = -4.936698586
x = -4.936698586

Simplifying
x = -4.936698586


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.063301414, -4.936698586}
Solution
x = {-0.063301414, -4.936698586}

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