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

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

Simplifying
2x(5 + x) + -2 = 6(x + -2) + 2x
(5 * 2x + x * 2x) + -2 = 6(x + -2) + 2x
(10x + 2x2) + -2 = 6(x + -2) + 2x

Reorder the terms:
-2 + 10x + 2x2 = 6(x + -2) + 2x

Reorder the terms:
-2 + 10x + 2x2 = 6(-2 + x) + 2x
-2 + 10x + 2x2 = (-2 * 6 + x * 6) + 2x
-2 + 10x + 2x2 = (-12 + 6x) + 2x

Combine like terms: 6x + 2x = 8x
-2 + 10x + 2x2 = -12 + 8x

Solving
-2 + 10x + 2x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
-2 + 12 + 10x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: -2 + 12 = 10
10 + 10x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: 10x + -8x = 2x
10 + 2x + 2x2 = -12 + 8x + 12 + -8x

Reorder the terms:
10 + 2x + 2x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
10 + 2x + 2x2 = 0 + 8x + -8x
10 + 2x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
10 + 2x + 2x2 = 0

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

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

Simplifying
5 + x + x2 = 0

Solving
5 + x + x2 = 0

Begin completing the square.

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.
x + 0.25 + x2 = -5 + 0.25

Reorder the terms:
0.25 + x + x2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + x + x2 = -4.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.