3x-4x(x-3)=3(x-4)

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


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

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

Combine like terms: 3x + 12x = 15x
15x + -4x2 = 3(x + -4)

Reorder the terms:
15x + -4x2 = 3(-4 + x)
15x + -4x2 = (-4 * 3 + x * 3)
15x + -4x2 = (-12 + 3x)

Solving
15x + -4x2 = -12 + 3x

Solving for variable 'x'.

Reorder the terms:
12 + 15x + -3x + -4x2 = -12 + 3x + 12 + -3x

Combine like terms: 15x + -3x = 12x
12 + 12x + -4x2 = -12 + 3x + 12 + -3x

Reorder the terms:
12 + 12x + -4x2 = -12 + 12 + 3x + -3x

Combine like terms: -12 + 12 = 0
12 + 12x + -4x2 = 0 + 3x + -3x
12 + 12x + -4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + 12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 3x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + 3x + -1x2 = 0

Solving
3 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-3 + -3x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3x + 3 + x2 = 0 + 3

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

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

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3x + x2 = 5.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + -1.5 = 2.291287847

Simplifying
x + -1.5 = 2.291287847

Reorder the terms:
-1.5 + x = 2.291287847

Solving
-1.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.291287847 + 1.5
x = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
x = 3.791287847

Simplifying
x = 3.791287847


Subproblem 2
x + -1.5 = -2.291287847

Simplifying
x + -1.5 = -2.291287847

Reorder the terms:
-1.5 + x = -2.291287847

Solving
-1.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.291287847 + 1.5
x = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
x = -0.791287847

Simplifying
x = -0.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.791287847, -0.791287847}
Solution
x = {3.791287847, -0.791287847}

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