4x(x-16)=20

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Solution for 4x(x-16)=20 equation: 


Simplifying
4x(x + -16) = 20

Reorder the terms:
4x(-16 + x) = 20
(-16 * 4x + x * 4x) = 20
(-64x + 4x2) = 20

Solving
-64x + 4x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -64x + 4x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -16x + x2) = 0

Ignore the factor 4.

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

Simplifying
-5 + -16x + x2 = 0

Solving
-5 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -16x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -16x + x2 = 0 + 5

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

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

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 5 + 64

Reorder the terms:
64 + -16x + x2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + -16x + x2 = 69

Factor a perfect square on the left side:
(x + -8)(x + -8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + -8) equal to 8.306623863 and -8.306623863.


Subproblem 1
x + -8 = 8.306623863

Simplifying
x + -8 = 8.306623863

Reorder the terms:
-8 + x = 8.306623863

Solving
-8 + x = 8.306623863

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 8.306623863 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.306623863 + 8
x = 8.306623863 + 8

Combine like terms: 8.306623863 + 8 = 16.306623863
x = 16.306623863

Simplifying
x = 16.306623863


Subproblem 2
x + -8 = -8.306623863

Simplifying
x + -8 = -8.306623863

Reorder the terms:
-8 + x = -8.306623863

Solving
-8 + x = -8.306623863

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -8.306623863 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.306623863 + 8
x = -8.306623863 + 8

Combine like terms: -8.306623863 + 8 = -0.306623863
x = -0.306623863

Simplifying
x = -0.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.306623863, -0.306623863}
Solution
x = {16.306623863, -0.306623863}

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