x(x+3)+50=2(x+3)(x-2)

Solution for x(x+3)+50=2(x+3)(x-2) equation:

Simplifying
x(x + 3) + 50 = 2(x + 3)(x + -2)

Reorder the terms:
x(3 + x) + 50 = 2(x + 3)(x + -2)
(3 * x + x * x) + 50 = 2(x + 3)(x + -2)
(3x + x2) + 50 = 2(x + 3)(x + -2)

Reorder the terms:
50 + 3x + x2 = 2(x + 3)(x + -2)

Reorder the terms:
50 + 3x + x2 = 2(3 + x)(x + -2)

Reorder the terms:
50 + 3x + x2 = 2(3 + x)(-2 + x)

Multiply (3 + x) * (-2 + x)
50 + 3x + x2 = 2(3(-2 + x) + x(-2 + x))
50 + 3x + x2 = 2((-2 * 3 + x * 3) + x(-2 + x))
50 + 3x + x2 = 2((-6 + 3x) + x(-2 + x))
50 + 3x + x2 = 2(-6 + 3x + (-2 * x + x * x))
50 + 3x + x2 = 2(-6 + 3x + (-2x + x2))

Combine like terms: 3x + -2x = 1x
50 + 3x + x2 = 2(-6 + 1x + x2)
50 + 3x + x2 = (-6 * 2 + 1x * 2 + x2 * 2)
50 + 3x + x2 = (-12 + 2x + 2x2)

Solving
50 + 3x + x2 = -12 + 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
50 + 12 + 3x + -2x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Combine like terms: 50 + 12 = 62
62 + 3x + -2x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Combine like terms: 3x + -2x = 1x
62 + 1x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Combine like terms: x2 + -2x2 = -1x2
62 + 1x + -1x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Reorder the terms:
62 + 1x + -1x2 = -12 + 12 + 2x + -2x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
62 + 1x + -1x2 = 0 + 2x + -2x + 2x2 + -2x2
62 + 1x + -1x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
62 + 1x + -1x2 = 0 + 2x2 + -2x2
62 + 1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
62 + 1x + -1x2 = 0

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

Divide each side by '-1'.
-62 + -1x + x2 = 0

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -1x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + -1x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -1x + x2 = 0 + 62
-1x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
-1x + x2 = 62

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 = 62 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 62 + 0.25

Combine like terms: 62 + 0.25 = 62.25
0.25 + -1x + x2 = 62.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -0.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
x + -0.5 = 7.889866919

Simplifying
x + -0.5 = 7.889866919

Reorder the terms:
-0.5 + x = 7.889866919

Solving
-0.5 + x = 7.889866919

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 = 7.889866919 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 7.889866919 + 0.5
x = 7.889866919 + 0.5

Combine like terms: 7.889866919 + 0.5 = 8.389866919
x = 8.389866919

Simplifying
x = 8.389866919

Subproblem 2
x + -0.5 = -7.889866919

Simplifying
x + -0.5 = -7.889866919

Reorder the terms:
-0.5 + x = -7.889866919

Solving
-0.5 + x = -7.889866919

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 = -7.889866919 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -7.889866919 + 0.5
x = -7.889866919 + 0.5

Combine like terms: -7.889866919 + 0.5 = -7.389866919
x = -7.389866919

Simplifying
x = -7.389866919

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.389866919, -7.389866919}