4x(2x-5)=20

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Solution for 4x(2x-5)=20 equation: 


Simplifying
4x(2x + -5) = 20

Reorder the terms:
4x(-5 + 2x) = 20
(-5 * 4x + 2x * 4x) = 20
(-20x + 8x2) = 20

Solving
-20x + 8x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -20x + 8x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -20x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -5x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + -5x + 2x2 = 0

Solving
-5 + -5x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2.5x + x2 = 0 + 2.5
-2.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2.5x + x2 = 2.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 2.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 2.5 + 1.5625

Combine like terms: 2.5 + 1.5625 = 4.0625
1.5625 + -2.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + -1.25 = 2.015564437

Simplifying
x + -1.25 = 2.015564437

Reorder the terms:
-1.25 + x = 2.015564437

Solving
-1.25 + x = 2.015564437

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.015564437 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.015564437 + 1.25
x = 2.015564437 + 1.25

Combine like terms: 2.015564437 + 1.25 = 3.265564437
x = 3.265564437

Simplifying
x = 3.265564437


Subproblem 2
x + -1.25 = -2.015564437

Simplifying
x + -1.25 = -2.015564437

Reorder the terms:
-1.25 + x = -2.015564437

Solving
-1.25 + x = -2.015564437

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.015564437 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.015564437 + 1.25
x = -2.015564437 + 1.25

Combine like terms: -2.015564437 + 1.25 = -0.765564437
x = -0.765564437

Simplifying
x = -0.765564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.265564437, -0.765564437}
Solution
x = {3.265564437, -0.765564437}

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