2x(2x-20)=6x+10

Solution for 2x(2x-20)=6x+10 equation:

Simplifying
2x(2x + -20) = 6x + 10

Reorder the terms:
2x(-20 + 2x) = 6x + 10
(-20 * 2x + 2x * 2x) = 6x + 10
(-40x + 4x2) = 6x + 10

Reorder the terms:
-40x + 4x2 = 10 + 6x

Solving
-40x + 4x2 = 10 + 6x

Solving for variable 'x'.

Reorder the terms:
-10 + -40x + -6x + 4x2 = 10 + 6x + -10 + -6x

Combine like terms: -40x + -6x = -46x
-10 + -46x + 4x2 = 10 + 6x + -10 + -6x

Reorder the terms:
-10 + -46x + 4x2 = 10 + -10 + 6x + -6x

Combine like terms: 10 + -10 = 0
-10 + -46x + 4x2 = 0 + 6x + -6x
-10 + -46x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-10 + -46x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -23x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -23x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + -23x + 2x2 = 0

Solving
-5 + -23x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -11.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -11.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -11.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -11.5x + x2 = 0 + 2.5
-11.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-11.5x + x2 = 2.5

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = 2.5 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = 2.5 + 33.0625

Combine like terms: 2.5 + 33.0625 = 35.5625
33.0625 + -11.5x + x2 = 35.5625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 35.5625

Calculate the square root of the right side: 5.963430221

Break this problem into two subproblems by setting 
(x + -5.75) equal to 5.963430221 and -5.963430221.

Subproblem 1
x + -5.75 = 5.963430221

Simplifying
x + -5.75 = 5.963430221

Reorder the terms:
-5.75 + x = 5.963430221

Solving
-5.75 + x = 5.963430221

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = 5.963430221 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = 5.963430221 + 5.75
x = 5.963430221 + 5.75

Combine like terms: 5.963430221 + 5.75 = 11.713430221
x = 11.713430221

Simplifying
x = 11.713430221

Subproblem 2
x + -5.75 = -5.963430221

Simplifying
x + -5.75 = -5.963430221

Reorder the terms:
-5.75 + x = -5.963430221

Solving
-5.75 + x = -5.963430221

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = -5.963430221 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = -5.963430221 + 5.75
x = -5.963430221 + 5.75

Combine like terms: -5.963430221 + 5.75 = -0.213430221
x = -0.213430221

Simplifying
x = -0.213430221

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.713430221, -0.213430221}
Solution
x = {11.713430221, -0.213430221}