2(-x+3)5x=x+20

Solution for 2(-x+3)5x=x+20 equation:

Simplifying
2(-1x + 3) * 5x = x + 20

Reorder the terms:
2(3 + -1x) * 5x = x + 20

Reorder the terms for easier multiplication:
2 * 5x(3 + -1x) = x + 20

Multiply 2 * 5
10x(3 + -1x) = x + 20
(3 * 10x + -1x * 10x) = x + 20
(30x + -10x2) = x + 20

Reorder the terms:
30x + -10x2 = 20 + x

Solving
30x + -10x2 = 20 + x

Solving for variable 'x'.

Reorder the terms:
-20 + 30x + -1x + -10x2 = 20 + x + -20 + -1x

Combine like terms: 30x + -1x = 29x
-20 + 29x + -10x2 = 20 + x + -20 + -1x

Reorder the terms:
-20 + 29x + -10x2 = 20 + -20 + x + -1x

Combine like terms: 20 + -20 = 0
-20 + 29x + -10x2 = 0 + x + -1x
-20 + 29x + -10x2 = x + -1x

Combine like terms: x + -1x = 0
-20 + 29x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
2 + -2.9x + x2 = 0.0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.9x + -2 + x2 = 0.0 + -2

Reorder the terms:
2 + -2 + -2.9x + x2 = 0.0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.9x + x2 = 0.0 + -2
-2.9x + x2 = 0.0 + -2

Combine like terms: 0.0 + -2 = -2
-2.9x + x2 = -2

The x term is -2.9x.  Take half its coefficient (-1.45).
Square it (2.1025) and add it to both sides.

Add '2.1025' to each side of the equation.
-2.9x + 2.1025 + x2 = -2 + 2.1025

Reorder the terms:
2.1025 + -2.9x + x2 = -2 + 2.1025

Combine like terms: -2 + 2.1025 = 0.1025
2.1025 + -2.9x + x2 = 0.1025

Factor a perfect square on the left side:
(x + -1.45)(x + -1.45) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(x + -1.45) equal to 0.320156212 and -0.320156212.

Subproblem 1
x + -1.45 = 0.320156212

Simplifying
x + -1.45 = 0.320156212

Reorder the terms:
-1.45 + x = 0.320156212

Solving
-1.45 + x = 0.320156212

Solving for variable 'x'.

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

Add '1.45' to each side of the equation.
-1.45 + 1.45 + x = 0.320156212 + 1.45

Combine like terms: -1.45 + 1.45 = 0.00
0.00 + x = 0.320156212 + 1.45
x = 0.320156212 + 1.45

Combine like terms: 0.320156212 + 1.45 = 1.770156212
x = 1.770156212

Simplifying
x = 1.770156212

Subproblem 2
x + -1.45 = -0.320156212

Simplifying
x + -1.45 = -0.320156212

Reorder the terms:
-1.45 + x = -0.320156212

Solving
-1.45 + x = -0.320156212

Solving for variable 'x'.

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

Add '1.45' to each side of the equation.
-1.45 + 1.45 + x = -0.320156212 + 1.45

Combine like terms: -1.45 + 1.45 = 0.00
0.00 + x = -0.320156212 + 1.45
x = -0.320156212 + 1.45

Combine like terms: -0.320156212 + 1.45 = 1.129843788
x = 1.129843788

Simplifying
x = 1.129843788

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.770156212, 1.129843788}