(5x-7)(3x+3)=12(x+1)-3x(9-x)

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Solution for (5x-7)(3x+3)=12(x+1)-3x(9-x) equation: 


Simplifying
(5x + -7)(3x + 3) = 12(x + 1) + -3x(9 + -1x)

Reorder the terms:
(-7 + 5x)(3x + 3) = 12(x + 1) + -3x(9 + -1x)

Reorder the terms:
(-7 + 5x)(3 + 3x) = 12(x + 1) + -3x(9 + -1x)

Multiply (-7 + 5x) * (3 + 3x)
(-7(3 + 3x) + 5x * (3 + 3x)) = 12(x + 1) + -3x(9 + -1x)
((3 * -7 + 3x * -7) + 5x * (3 + 3x)) = 12(x + 1) + -3x(9 + -1x)
((-21 + -21x) + 5x * (3 + 3x)) = 12(x + 1) + -3x(9 + -1x)
(-21 + -21x + (3 * 5x + 3x * 5x)) = 12(x + 1) + -3x(9 + -1x)
(-21 + -21x + (15x + 15x2)) = 12(x + 1) + -3x(9 + -1x)

Combine like terms: -21x + 15x = -6x
(-21 + -6x + 15x2) = 12(x + 1) + -3x(9 + -1x)

Reorder the terms:
-21 + -6x + 15x2 = 12(1 + x) + -3x(9 + -1x)
-21 + -6x + 15x2 = (1 * 12 + x * 12) + -3x(9 + -1x)
-21 + -6x + 15x2 = (12 + 12x) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12 + 12x + (9 * -3x + -1x * -3x)
-21 + -6x + 15x2 = 12 + 12x + (-27x + 3x2)

Combine like terms: 12x + -27x = -15x
-21 + -6x + 15x2 = 12 + -15x + 3x2

Solving
-21 + -6x + 15x2 = 12 + -15x + 3x2

Solving for variable 'x'.

Reorder the terms:
-21 + -12 + -6x + 15x + 15x2 + -3x2 = 12 + -15x + 3x2 + -12 + 15x + -3x2

Combine like terms: -21 + -12 = -33
-33 + -6x + 15x + 15x2 + -3x2 = 12 + -15x + 3x2 + -12 + 15x + -3x2

Combine like terms: -6x + 15x = 9x
-33 + 9x + 15x2 + -3x2 = 12 + -15x + 3x2 + -12 + 15x + -3x2

Combine like terms: 15x2 + -3x2 = 12x2
-33 + 9x + 12x2 = 12 + -15x + 3x2 + -12 + 15x + -3x2

Reorder the terms:
-33 + 9x + 12x2 = 12 + -12 + -15x + 15x + 3x2 + -3x2

Combine like terms: 12 + -12 = 0
-33 + 9x + 12x2 = 0 + -15x + 15x + 3x2 + -3x2
-33 + 9x + 12x2 = -15x + 15x + 3x2 + -3x2

Combine like terms: -15x + 15x = 0
-33 + 9x + 12x2 = 0 + 3x2 + -3x2
-33 + 9x + 12x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-33 + 9x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 3x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-11 + 3x + 4x2 = 0

Solving
-11 + 3x + 4x2 = 0

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

Divide each side by '4'.
-2.75 + 0.75x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 0.75x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 0.75x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 0.75x + x2 = 0 + 2.75
0.75x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
0.75x + x2 = 2.75

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 2.75 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 2.75 + 0.140625

Combine like terms: 2.75 + 0.140625 = 2.890625
0.140625 + 0.75x + x2 = 2.890625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.700183814 and -1.700183814.


Subproblem 1
x + 0.375 = 1.700183814

Simplifying
x + 0.375 = 1.700183814

Reorder the terms:
0.375 + x = 1.700183814

Solving
0.375 + x = 1.700183814

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.700183814 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.700183814 + -0.375
x = 1.700183814 + -0.375

Combine like terms: 1.700183814 + -0.375 = 1.325183814
x = 1.325183814

Simplifying
x = 1.325183814


Subproblem 2
x + 0.375 = -1.700183814

Simplifying
x + 0.375 = -1.700183814

Reorder the terms:
0.375 + x = -1.700183814

Solving
0.375 + x = -1.700183814

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.700183814 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.700183814 + -0.375
x = -1.700183814 + -0.375

Combine like terms: -1.700183814 + -0.375 = -2.075183814
x = -2.075183814

Simplifying
x = -2.075183814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.325183814, -2.075183814}
Solution
x = {1.325183814, -2.075183814}

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