2x(-x+6)+3(x-1)=0

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Solution for 2x(-x+6)+3(x-1)=0 equation: 


Simplifying
2x(-1x + 6) + 3(x + -1) = 0

Reorder the terms:
2x(6 + -1x) + 3(x + -1) = 0
(6 * 2x + -1x * 2x) + 3(x + -1) = 0
(12x + -2x2) + 3(x + -1) = 0

Reorder the terms:
12x + -2x2 + 3(-1 + x) = 0
12x + -2x2 + (-1 * 3 + x * 3) = 0
12x + -2x2 + (-3 + 3x) = 0

Reorder the terms:
-3 + 12x + 3x + -2x2 = 0

Combine like terms: 12x + 3x = 15x
-3 + 15x + -2x2 = 0

Solving
-3 + 15x + -2x2 = 0

Solving for variable 'x'.

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

Divide each side by '-2'.
1.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -7.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -7.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -7.5x + x2 = 0 + -1.5
-7.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-7.5x + x2 = -1.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -1.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -1.5 + 14.0625

Combine like terms: -1.5 + 14.0625 = 12.5625
14.0625 + -7.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.54436172 and -3.54436172.


Subproblem 1
x + -3.75 = 3.54436172

Simplifying
x + -3.75 = 3.54436172

Reorder the terms:
-3.75 + x = 3.54436172

Solving
-3.75 + x = 3.54436172

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.54436172 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.54436172 + 3.75
x = 3.54436172 + 3.75

Combine like terms: 3.54436172 + 3.75 = 7.29436172
x = 7.29436172

Simplifying
x = 7.29436172


Subproblem 2
x + -3.75 = -3.54436172

Simplifying
x + -3.75 = -3.54436172

Reorder the terms:
-3.75 + x = -3.54436172

Solving
-3.75 + x = -3.54436172

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.54436172 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.54436172 + 3.75
x = -3.54436172 + 3.75

Combine like terms: -3.54436172 + 3.75 = 0.20563828
x = 0.20563828

Simplifying
x = 0.20563828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.29436172, 0.20563828}

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