x(1-2x)=3(x-5)

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Solution for x(1-2x)=3(x-5) equation: 


Simplifying
x(1 + -2x) = 3(x + -5)
(1 * x + -2x * x) = 3(x + -5)
(1x + -2x2) = 3(x + -5)

Reorder the terms:
1x + -2x2 = 3(-5 + x)
1x + -2x2 = (-5 * 3 + x * 3)
1x + -2x2 = (-15 + 3x)

Solving
1x + -2x2 = -15 + 3x

Solving for variable 'x'.

Reorder the terms:
15 + 1x + -3x + -2x2 = -15 + 3x + 15 + -3x

Combine like terms: 1x + -3x = -2x
15 + -2x + -2x2 = -15 + 3x + 15 + -3x

Reorder the terms:
15 + -2x + -2x2 = -15 + 15 + 3x + -3x

Combine like terms: -15 + 15 = 0
15 + -2x + -2x2 = 0 + 3x + -3x
15 + -2x + -2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
15 + -2x + -2x2 = 0

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

Divide each side by '-2'.
-7.5 + x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x + x2 = 0 + 7.5
x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
x + x2 = 7.5

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 = 7.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 7.5 + 0.25

Combine like terms: 7.5 + 0.25 = 7.75
1.25 + x2 = 7.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.783882181 and -2.783882181.


Subproblem 1
x + 0.5 = 2.783882181

Simplifying
x + 0.5 = 2.783882181

Reorder the terms:
0.5 + x = 2.783882181

Solving
0.5 + x = 2.783882181

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 = 2.783882181 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.783882181 + -0.5
x = 2.783882181 + -0.5

Combine like terms: 2.783882181 + -0.5 = 2.283882181
x = 2.283882181

Simplifying
x = 2.283882181


Subproblem 2
x + 0.5 = -2.783882181

Simplifying
x + 0.5 = -2.783882181

Reorder the terms:
0.5 + x = -2.783882181

Solving
0.5 + x = -2.783882181

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 = -2.783882181 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.783882181 + -0.5
x = -2.783882181 + -0.5

Combine like terms: -2.783882181 + -0.5 = -3.283882181
x = -3.283882181

Simplifying
x = -3.283882181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.283882181, -3.283882181}

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