4(x-3)(3x-5)=-3(x^2-4x+4)

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Solution for 4(x-3)(3x-5)=-3(x^2-4x+4) equation: 


Simplifying
4(x + -3)(3x + -5) = -3(x2 + -4x + 4)

Reorder the terms:
4(-3 + x)(3x + -5) = -3(x2 + -4x + 4)

Reorder the terms:
4(-3 + x)(-5 + 3x) = -3(x2 + -4x + 4)

Multiply (-3 + x) * (-5 + 3x)
4(-3(-5 + 3x) + x(-5 + 3x)) = -3(x2 + -4x + 4)
4((-5 * -3 + 3x * -3) + x(-5 + 3x)) = -3(x2 + -4x + 4)
4((15 + -9x) + x(-5 + 3x)) = -3(x2 + -4x + 4)
4(15 + -9x + (-5 * x + 3x * x)) = -3(x2 + -4x + 4)
4(15 + -9x + (-5x + 3x2)) = -3(x2 + -4x + 4)

Combine like terms: -9x + -5x = -14x
4(15 + -14x + 3x2) = -3(x2 + -4x + 4)
(15 * 4 + -14x * 4 + 3x2 * 4) = -3(x2 + -4x + 4)
(60 + -56x + 12x2) = -3(x2 + -4x + 4)

Reorder the terms:
60 + -56x + 12x2 = -3(4 + -4x + x2)
60 + -56x + 12x2 = (4 * -3 + -4x * -3 + x2 * -3)
60 + -56x + 12x2 = (-12 + 12x + -3x2)

Solving
60 + -56x + 12x2 = -12 + 12x + -3x2

Solving for variable 'x'.

Reorder the terms:
60 + 12 + -56x + -12x + 12x2 + 3x2 = -12 + 12x + -3x2 + 12 + -12x + 3x2

Combine like terms: 60 + 12 = 72
72 + -56x + -12x + 12x2 + 3x2 = -12 + 12x + -3x2 + 12 + -12x + 3x2

Combine like terms: -56x + -12x = -68x
72 + -68x + 12x2 + 3x2 = -12 + 12x + -3x2 + 12 + -12x + 3x2

Combine like terms: 12x2 + 3x2 = 15x2
72 + -68x + 15x2 = -12 + 12x + -3x2 + 12 + -12x + 3x2

Reorder the terms:
72 + -68x + 15x2 = -12 + 12 + 12x + -12x + -3x2 + 3x2

Combine like terms: -12 + 12 = 0
72 + -68x + 15x2 = 0 + 12x + -12x + -3x2 + 3x2
72 + -68x + 15x2 = 12x + -12x + -3x2 + 3x2

Combine like terms: 12x + -12x = 0
72 + -68x + 15x2 = 0 + -3x2 + 3x2
72 + -68x + 15x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
72 + -68x + 15x2 = 0

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

Divide each side by '15'.
4.8 + -4.533333333x + x2 = 0

Move the constant term to the right:

Add '-4.8' to each side of the equation.
4.8 + -4.533333333x + -4.8 + x2 = 0 + -4.8

Reorder the terms:
4.8 + -4.8 + -4.533333333x + x2 = 0 + -4.8

Combine like terms: 4.8 + -4.8 = 0.0
0.0 + -4.533333333x + x2 = 0 + -4.8
-4.533333333x + x2 = 0 + -4.8

Combine like terms: 0 + -4.8 = -4.8
-4.533333333x + x2 = -4.8

The x term is -4.533333333x.  Take half its coefficient (-2.266666667).
Square it (5.137777779) and add it to both sides.

Add '5.137777779' to each side of the equation.
-4.533333333x + 5.137777779 + x2 = -4.8 + 5.137777779

Reorder the terms:
5.137777779 + -4.533333333x + x2 = -4.8 + 5.137777779

Combine like terms: -4.8 + 5.137777779 = 0.337777779
5.137777779 + -4.533333333x + x2 = 0.337777779

Factor a perfect square on the left side:
(x + -2.266666667)(x + -2.266666667) = 0.337777779

Calculate the square root of the right side: 0.581186527

Break this problem into two subproblems by setting 
(x + -2.266666667) equal to 0.581186527 and -0.581186527.


Subproblem 1
x + -2.266666667 = 0.581186527

Simplifying
x + -2.266666667 = 0.581186527

Reorder the terms:
-2.266666667 + x = 0.581186527

Solving
-2.266666667 + x = 0.581186527

Solving for variable 'x'.

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

Add '2.266666667' to each side of the equation.
-2.266666667 + 2.266666667 + x = 0.581186527 + 2.266666667

Combine like terms: -2.266666667 + 2.266666667 = 0.000000000
0.000000000 + x = 0.581186527 + 2.266666667
x = 0.581186527 + 2.266666667

Combine like terms: 0.581186527 + 2.266666667 = 2.847853194
x = 2.847853194

Simplifying
x = 2.847853194


Subproblem 2
x + -2.266666667 = -0.581186527

Simplifying
x + -2.266666667 = -0.581186527

Reorder the terms:
-2.266666667 + x = -0.581186527

Solving
-2.266666667 + x = -0.581186527

Solving for variable 'x'.

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

Add '2.266666667' to each side of the equation.
-2.266666667 + 2.266666667 + x = -0.581186527 + 2.266666667

Combine like terms: -2.266666667 + 2.266666667 = 0.000000000
0.000000000 + x = -0.581186527 + 2.266666667
x = -0.581186527 + 2.266666667

Combine like terms: -0.581186527 + 2.266666667 = 1.68548014
x = 1.68548014

Simplifying
x = 1.68548014


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.847853194, 1.68548014}

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