5x(3x+28)=180

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Solution for 5x(3x+28)=180 equation: 


Simplifying
5x(3x + 28) = 180

Reorder the terms:
5x(28 + 3x) = 180
(28 * 5x + 3x * 5x) = 180
(140x + 15x2) = 180

Solving
140x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 140x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 140x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 28x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-36 + 28x + 3x2)' equal to zero and attempt to solve:

Simplifying
-36 + 28x + 3x2 = 0

Solving
-36 + 28x + 3x2 = 0

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

Divide each side by '3'.
-12 + 9.333333333x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 9.333333333x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 9.333333333x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 9.333333333x + x2 = 0 + 12
9.333333333x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
9.333333333x + x2 = 12

The x term is 9.333333333x.  Take half its coefficient (4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
9.333333333x + 21.77777778 + x2 = 12 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333x + x2 = 12 + 21.77777778

Combine like terms: 12 + 21.77777778 = 33.77777778
21.77777778 + 9.333333333x + x2 = 33.77777778

Factor a perfect square on the left side:
(x + 4.666666667)(x + 4.666666667) = 33.77777778

Calculate the square root of the right side: 5.811865258

Break this problem into two subproblems by setting 
(x + 4.666666667) equal to 5.811865258 and -5.811865258.


Subproblem 1
x + 4.666666667 = 5.811865258

Simplifying
x + 4.666666667 = 5.811865258

Reorder the terms:
4.666666667 + x = 5.811865258

Solving
4.666666667 + x = 5.811865258

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x = 5.811865258 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = 5.811865258 + -4.666666667
x = 5.811865258 + -4.666666667

Combine like terms: 5.811865258 + -4.666666667 = 1.145198591
x = 1.145198591

Simplifying
x = 1.145198591


Subproblem 2
x + 4.666666667 = -5.811865258

Simplifying
x + 4.666666667 = -5.811865258

Reorder the terms:
4.666666667 + x = -5.811865258

Solving
4.666666667 + x = -5.811865258

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x = -5.811865258 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = -5.811865258 + -4.666666667
x = -5.811865258 + -4.666666667

Combine like terms: -5.811865258 + -4.666666667 = -10.478531925
x = -10.478531925

Simplifying
x = -10.478531925


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.145198591, -10.478531925}
Solution
x = {1.145198591, -10.478531925}

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