x(2x-8)=60

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Solution for x(2x-8)=60 equation: 


Simplifying
x(2x + -8) = 60

Reorder the terms:
x(-8 + 2x) = 60
(-8 * x + 2x * x) = 60
(-8x + 2x2) = 60

Solving
-8x + 2x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -8x + 2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + -4x + x2 = 0

Solving
-30 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -4x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -4x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -4x + x2 = 0 + 30
-4x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-4x + x2 = 30

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 30 + 4

Reorder the terms:
4 + -4x + x2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + -4x + x2 = 34

Factor a perfect square on the left side:
(x + -2)(x + -2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -2) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + -2 = 5.830951895

Simplifying
x + -2 = 5.830951895

Reorder the terms:
-2 + x = 5.830951895

Solving
-2 + x = 5.830951895

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.830951895 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.830951895 + 2
x = 5.830951895 + 2

Combine like terms: 5.830951895 + 2 = 7.830951895
x = 7.830951895

Simplifying
x = 7.830951895


Subproblem 2
x + -2 = -5.830951895

Simplifying
x + -2 = -5.830951895

Reorder the terms:
-2 + x = -5.830951895

Solving
-2 + x = -5.830951895

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.830951895 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.830951895 + 2
x = -5.830951895 + 2

Combine like terms: -5.830951895 + 2 = -3.830951895
x = -3.830951895

Simplifying
x = -3.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.830951895, -3.830951895}
Solution
x = {7.830951895, -3.830951895}

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