(3x-7)(2x+2)=180

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Solution for (3x-7)(2x+2)=180 equation: 


Simplifying
(3x + -7)(2x + 2) = 180

Reorder the terms:
(-7 + 3x)(2x + 2) = 180

Reorder the terms:
(-7 + 3x)(2 + 2x) = 180

Multiply (-7 + 3x) * (2 + 2x)
(-7(2 + 2x) + 3x * (2 + 2x)) = 180
((2 * -7 + 2x * -7) + 3x * (2 + 2x)) = 180
((-14 + -14x) + 3x * (2 + 2x)) = 180
(-14 + -14x + (2 * 3x + 2x * 3x)) = 180
(-14 + -14x + (6x + 6x2)) = 180

Combine like terms: -14x + 6x = -8x
(-14 + -8x + 6x2) = 180

Solving
-14 + -8x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-14 + -180 + -8x + 6x2 = 180 + -180

Combine like terms: -14 + -180 = -194
-194 + -8x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-194 + -8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-97 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-97 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-97 + -4x + 3x2 = 0

Solving
-97 + -4x + 3x2 = 0

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

Divide each side by '3'.
-32.33333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '32.33333333' to each side of the equation.
-32.33333333 + -1.333333333x + 32.33333333 + x2 = 0 + 32.33333333

Reorder the terms:
-32.33333333 + 32.33333333 + -1.333333333x + x2 = 0 + 32.33333333

Combine like terms: -32.33333333 + 32.33333333 = 0.00000000
0.00000000 + -1.333333333x + x2 = 0 + 32.33333333
-1.333333333x + x2 = 0 + 32.33333333

Combine like terms: 0 + 32.33333333 = 32.33333333
-1.333333333x + x2 = 32.33333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 32.33333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 32.33333333 + 0.4444444442

Combine like terms: 32.33333333 + 0.4444444442 = 32.7777777742
0.4444444442 + -1.333333333x + x2 = 32.7777777742

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 32.7777777742

Calculate the square root of the right side: 5.725188012

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 5.725188012 and -5.725188012.


Subproblem 1
x + -0.6666666665 = 5.725188012

Simplifying
x + -0.6666666665 = 5.725188012

Reorder the terms:
-0.6666666665 + x = 5.725188012

Solving
-0.6666666665 + x = 5.725188012

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 5.725188012 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 5.725188012 + 0.6666666665
x = 5.725188012 + 0.6666666665

Combine like terms: 5.725188012 + 0.6666666665 = 6.3918546785
x = 6.3918546785

Simplifying
x = 6.3918546785


Subproblem 2
x + -0.6666666665 = -5.725188012

Simplifying
x + -0.6666666665 = -5.725188012

Reorder the terms:
-0.6666666665 + x = -5.725188012

Solving
-0.6666666665 + x = -5.725188012

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -5.725188012 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -5.725188012 + 0.6666666665
x = -5.725188012 + 0.6666666665

Combine like terms: -5.725188012 + 0.6666666665 = -5.0585213455
x = -5.0585213455

Simplifying
x = -5.0585213455


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.3918546785, -5.0585213455}
Solution
x = {6.3918546785, -5.0585213455}

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