(3x+28)(4x-2)=180

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Solution for (3x+28)(4x-2)=180 equation: 


Simplifying
(3x + 28)(4x + -2) = 180

Reorder the terms:
(28 + 3x)(4x + -2) = 180

Reorder the terms:
(28 + 3x)(-2 + 4x) = 180

Multiply (28 + 3x) * (-2 + 4x)
(28(-2 + 4x) + 3x * (-2 + 4x)) = 180
((-2 * 28 + 4x * 28) + 3x * (-2 + 4x)) = 180
((-56 + 112x) + 3x * (-2 + 4x)) = 180
(-56 + 112x + (-2 * 3x + 4x * 3x)) = 180
(-56 + 112x + (-6x + 12x2)) = 180

Combine like terms: 112x + -6x = 106x
(-56 + 106x + 12x2) = 180

Solving
-56 + 106x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-56 + -180 + 106x + 12x2 = 180 + -180

Combine like terms: -56 + -180 = -236
-236 + 106x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-236 + 106x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-118 + 53x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-118 + 53x + 6x2)' equal to zero and attempt to solve:

Simplifying
-118 + 53x + 6x2 = 0

Solving
-118 + 53x + 6x2 = 0

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

Divide each side by '6'.
-19.66666667 + 8.833333333x + x2 = 0

Move the constant term to the right:

Add '19.66666667' to each side of the equation.
-19.66666667 + 8.833333333x + 19.66666667 + x2 = 0 + 19.66666667

Reorder the terms:
-19.66666667 + 19.66666667 + 8.833333333x + x2 = 0 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + 8.833333333x + x2 = 0 + 19.66666667
8.833333333x + x2 = 0 + 19.66666667

Combine like terms: 0 + 19.66666667 = 19.66666667
8.833333333x + x2 = 19.66666667

The x term is 8.833333333x.  Take half its coefficient (4.416666667).
Square it (19.50694445) and add it to both sides.

Add '19.50694445' to each side of the equation.
8.833333333x + 19.50694445 + x2 = 19.66666667 + 19.50694445

Reorder the terms:
19.50694445 + 8.833333333x + x2 = 19.66666667 + 19.50694445

Combine like terms: 19.66666667 + 19.50694445 = 39.17361112
19.50694445 + 8.833333333x + x2 = 39.17361112

Factor a perfect square on the left side:
(x + 4.416666667)(x + 4.416666667) = 39.17361112

Calculate the square root of the right side: 6.258882578

Break this problem into two subproblems by setting 
(x + 4.416666667) equal to 6.258882578 and -6.258882578.


Subproblem 1
x + 4.416666667 = 6.258882578

Simplifying
x + 4.416666667 = 6.258882578

Reorder the terms:
4.416666667 + x = 6.258882578

Solving
4.416666667 + x = 6.258882578

Solving for variable 'x'.

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

Add '-4.416666667' to each side of the equation.
4.416666667 + -4.416666667 + x = 6.258882578 + -4.416666667

Combine like terms: 4.416666667 + -4.416666667 = 0.000000000
0.000000000 + x = 6.258882578 + -4.416666667
x = 6.258882578 + -4.416666667

Combine like terms: 6.258882578 + -4.416666667 = 1.842215911
x = 1.842215911

Simplifying
x = 1.842215911


Subproblem 2
x + 4.416666667 = -6.258882578

Simplifying
x + 4.416666667 = -6.258882578

Reorder the terms:
4.416666667 + x = -6.258882578

Solving
4.416666667 + x = -6.258882578

Solving for variable 'x'.

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

Add '-4.416666667' to each side of the equation.
4.416666667 + -4.416666667 + x = -6.258882578 + -4.416666667

Combine like terms: 4.416666667 + -4.416666667 = 0.000000000
0.000000000 + x = -6.258882578 + -4.416666667
x = -6.258882578 + -4.416666667

Combine like terms: -6.258882578 + -4.416666667 = -10.675549245
x = -10.675549245

Simplifying
x = -10.675549245


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.842215911, -10.675549245}
Solution
x = {1.842215911, -10.675549245}

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