4x(3x+20)=180

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Solution for 4x(3x+20)=180 equation: 


Simplifying
4x(3x + 20) = 180

Reorder the terms:
4x(20 + 3x) = 180
(20 * 4x + 3x * 4x) = 180
(80x + 12x2) = 180

Solving
80x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 80x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 80x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 20x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-45 + 20x + 3x2 = 0

Solving
-45 + 20x + 3x2 = 0

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

Divide each side by '3'.
-15 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 6.666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 6.666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 6.666666667x + x2 = 0 + 15
6.666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
6.666666667x + x2 = 15

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 15 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 15 + 11.11111112

Combine like terms: 15 + 11.11111112 = 26.11111112
11.11111112 + 6.666666667x + x2 = 26.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 26.11111112

Calculate the square root of the right side: 5.10990324

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 5.10990324 and -5.10990324.


Subproblem 1
x + 3.333333334 = 5.10990324

Simplifying
x + 3.333333334 = 5.10990324

Reorder the terms:
3.333333334 + x = 5.10990324

Solving
3.333333334 + x = 5.10990324

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 5.10990324 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 5.10990324 + -3.333333334
x = 5.10990324 + -3.333333334

Combine like terms: 5.10990324 + -3.333333334 = 1.776569906
x = 1.776569906

Simplifying
x = 1.776569906


Subproblem 2
x + 3.333333334 = -5.10990324

Simplifying
x + 3.333333334 = -5.10990324

Reorder the terms:
3.333333334 + x = -5.10990324

Solving
3.333333334 + x = -5.10990324

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -5.10990324 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -5.10990324 + -3.333333334
x = -5.10990324 + -3.333333334

Combine like terms: -5.10990324 + -3.333333334 = -8.443236574
x = -8.443236574

Simplifying
x = -8.443236574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.776569906, -8.443236574}
Solution
x = {1.776569906, -8.443236574}

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