2x(3)+2x(2)-60x=2x(x+6)(x-5)

Solution for 2x(3)+2x(2)-60x=2x(x+6)(x-5) equation:

Simplifying
2x(3) + 2x(2) + -60x = 2x(x + 6)(x + -5)

Reorder the terms for easier multiplication:
2 * 3x + 2x(2) + -60x = 2x(x + 6)(x + -5)

Multiply 2 * 3
6x + 2x(2) + -60x = 2x(x + 6)(x + -5)

Reorder the terms for easier multiplication:
6x + 2 * 2x + -60x = 2x(x + 6)(x + -5)

Multiply 2 * 2
6x + 4x + -60x = 2x(x + 6)(x + -5)

Combine like terms: 6x + 4x = 10x
10x + -60x = 2x(x + 6)(x + -5)

Combine like terms: 10x + -60x = -50x
-50x = 2x(x + 6)(x + -5)

Reorder the terms:
-50x = 2x(6 + x)(x + -5)

Reorder the terms:
-50x = 2x(6 + x)(-5 + x)

Multiply (6 + x) * (-5 + x)
-50x = 2x(6(-5 + x) + x(-5 + x))
-50x = 2x((-5 * 6 + x * 6) + x(-5 + x))
-50x = 2x((-30 + 6x) + x(-5 + x))
-50x = 2x(-30 + 6x + (-5 * x + x * x))
-50x = 2x(-30 + 6x + (-5x + x2))

Combine like terms: 6x + -5x = 1x
-50x = 2x(-30 + 1x + x2)
-50x = (-30 * 2x + 1x * 2x + x2 * 2x)
-50x = (-60x + 2x2 + 2x3)

Solving
-50x = -60x + 2x2 + 2x3

Solving for variable 'x'.

Combine like terms: -50x + 60x = 10x
10x + -2x2 + -2x3 = -60x + 2x2 + 2x3 + 60x + -2x2 + -2x3

Reorder the terms:
10x + -2x2 + -2x3 = -60x + 60x + 2x2 + -2x2 + 2x3 + -2x3

Combine like terms: -60x + 60x = 0
10x + -2x2 + -2x3 = 0 + 2x2 + -2x2 + 2x3 + -2x3
10x + -2x2 + -2x3 = 2x2 + -2x2 + 2x3 + -2x3

Combine like terms: 2x2 + -2x2 = 0
10x + -2x2 + -2x3 = 0 + 2x3 + -2x3
10x + -2x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
10x + -2x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + -1x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x + -1x2 = 0

Solving
5 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x + x2 = 0 + 5
x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
x + x2 = 5

The x term is x.  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.
 + 0.25 + x2 = 5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
1.25 + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 0.5 = 2.291287847

Simplifying
x + 0.5 = 2.291287847

Reorder the terms:
0.5 + x = 2.291287847

Solving
0.5 + x = 2.291287847

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 = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.291287847 + -0.5
x = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
x = 1.791287847

Simplifying
x = 1.791287847

Subproblem 2
x + 0.5 = -2.291287847

Simplifying
x + 0.5 = -2.291287847

Reorder the terms:
0.5 + x = -2.291287847

Solving
0.5 + x = -2.291287847

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 = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.291287847 + -0.5
x = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
x = -2.791287847

Simplifying
x = -2.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.791287847, -2.791287847}
Solution
x = {0, 1.791287847, -2.791287847}