3(x)(x-4)=765

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Solution for 3(x)(x-4)=765 equation: 


Simplifying
3(x)(x + -4) = 765

Reorder the terms:
3x(-4 + x) = 765
(-4 * 3x + x * 3x) = 765
(-12x + 3x2) = 765

Solving
-12x + 3x2 = 765

Solving for variable 'x'.

Reorder the terms:
-765 + -12x + 3x2 = 765 + -765

Combine like terms: 765 + -765 = 0
-765 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-255 + -4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-255 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-255 + -4x + x2 = 0

Solving
-255 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + -4x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + -4x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + -4x + x2 = 0 + 255
-4x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
-4x + x2 = 255

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 255 + 4

Reorder the terms:
4 + -4x + x2 = 255 + 4

Combine like terms: 255 + 4 = 259
4 + -4x + x2 = 259

Factor a perfect square on the left side:
(x + -2)(x + -2) = 259

Calculate the square root of the right side: 16.093476939

Break this problem into two subproblems by setting 
(x + -2) equal to 16.093476939 and -16.093476939.


Subproblem 1
x + -2 = 16.093476939

Simplifying
x + -2 = 16.093476939

Reorder the terms:
-2 + x = 16.093476939

Solving
-2 + x = 16.093476939

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 16.093476939 + 2

Combine like terms: -2 + 2 = 0
0 + x = 16.093476939 + 2
x = 16.093476939 + 2

Combine like terms: 16.093476939 + 2 = 18.093476939
x = 18.093476939

Simplifying
x = 18.093476939


Subproblem 2
x + -2 = -16.093476939

Simplifying
x + -2 = -16.093476939

Reorder the terms:
-2 + x = -16.093476939

Solving
-2 + x = -16.093476939

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -16.093476939 + 2

Combine like terms: -2 + 2 = 0
0 + x = -16.093476939 + 2
x = -16.093476939 + 2

Combine like terms: -16.093476939 + 2 = -14.093476939
x = -14.093476939

Simplifying
x = -14.093476939


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.093476939, -14.093476939}
Solution
x = {18.093476939, -14.093476939}

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