60=x(4x-10)

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Solution for 60=x(4x-10) equation: 


Simplifying
60 = x(4x + -10)

Reorder the terms:
60 = x(-10 + 4x)
60 = (-10 * x + 4x * x)
60 = (-10x + 4x2)

Solving
60 = -10x + 4x2

Solving for variable 'x'.

Reorder the terms:
60 + 10x + -4x2 = -10x + 10x + 4x2 + -4x2

Combine like terms: -10x + 10x = 0
60 + 10x + -4x2 = 0 + 4x2 + -4x2
60 + 10x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
60 + 10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + 5x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + 5x + -2x2)' equal to zero and attempt to solve:

Simplifying
30 + 5x + -2x2 = 0

Solving
30 + 5x + -2x2 = 0

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

Divide each side by '-2'.
-15 + -2.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -2.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -2.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2.5x + x2 = 0 + 15
-2.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-2.5x + x2 = 15

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 = 15 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 15 + 1.5625

Combine like terms: 15 + 1.5625 = 16.5625
1.5625 + -2.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + -1.25) equal to 4.069705149 and -4.069705149.


Subproblem 1
x + -1.25 = 4.069705149

Simplifying
x + -1.25 = 4.069705149

Reorder the terms:
-1.25 + x = 4.069705149

Solving
-1.25 + x = 4.069705149

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 = 4.069705149 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 4.069705149 + 1.25
x = 4.069705149 + 1.25

Combine like terms: 4.069705149 + 1.25 = 5.319705149
x = 5.319705149

Simplifying
x = 5.319705149


Subproblem 2
x + -1.25 = -4.069705149

Simplifying
x + -1.25 = -4.069705149

Reorder the terms:
-1.25 + x = -4.069705149

Solving
-1.25 + x = -4.069705149

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 = -4.069705149 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -4.069705149 + 1.25
x = -4.069705149 + 1.25

Combine like terms: -4.069705149 + 1.25 = -2.819705149
x = -2.819705149

Simplifying
x = -2.819705149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.319705149, -2.819705149}
Solution
x = {5.319705149, -2.819705149}

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