6x(10x-10)-8=

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Solution for 6x(10x-10)-8= equation: 


Simplifying
6x(10x + -10) + -8 = 0

Reorder the terms:
6x(-10 + 10x) + -8 = 0
(-10 * 6x + 10x * 6x) + -8 = 0
(-60x + 60x2) + -8 = 0

Reorder the terms:
-8 + -60x + 60x2 = 0

Solving
-8 + -60x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -15x + 15x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -15x + 15x2)' equal to zero and attempt to solve:

Simplifying
-2 + -15x + 15x2 = 0

Solving
-2 + -15x + 15x2 = 0

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

Divide each side by '15'.
-0.1333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -1x + 0.1333333333 + x2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -1x + x2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.1333333333
-1x + x2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
-1x + x2 = 0.1333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.1333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.1333333333 + 0.25

Combine like terms: 0.1333333333 + 0.25 = 0.3833333333
0.25 + -1x + x2 = 0.3833333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.3833333333

Calculate the square root of the right side: 0.619139187

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.619139187 and -0.619139187.


Subproblem 1
x + -0.5 = 0.619139187

Simplifying
x + -0.5 = 0.619139187

Reorder the terms:
-0.5 + x = 0.619139187

Solving
-0.5 + x = 0.619139187

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.619139187 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.619139187 + 0.5
x = 0.619139187 + 0.5

Combine like terms: 0.619139187 + 0.5 = 1.119139187
x = 1.119139187

Simplifying
x = 1.119139187


Subproblem 2
x + -0.5 = -0.619139187

Simplifying
x + -0.5 = -0.619139187

Reorder the terms:
-0.5 + x = -0.619139187

Solving
-0.5 + x = -0.619139187

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.619139187 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.619139187 + 0.5
x = -0.619139187 + 0.5

Combine like terms: -0.619139187 + 0.5 = -0.119139187
x = -0.119139187

Simplifying
x = -0.119139187


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.119139187, -0.119139187}
Solution
x = {1.119139187, -0.119139187}

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