5x(3x+20)=180

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Solution for 5x(3x+20)=180 equation: 


Simplifying
5x(3x + 20) = 180

Reorder the terms:
5x(20 + 3x) = 180
(20 * 5x + 3x * 5x) = 180
(100x + 15x2) = 180

Solving
100x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 100x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 100x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 20x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-36 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-36 + 20x + 3x2 = 0

Solving
-36 + 20x + 3x2 = 0

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

Divide each side by '3'.
-12 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 6.666666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 6.666666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 6.666666667x + x2 = 0 + 12
6.666666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
6.666666667x + x2 = 12

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 = 12 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 12 + 11.11111112

Combine like terms: 12 + 11.11111112 = 23.11111112
11.11111112 + 6.666666667x + x2 = 23.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 23.11111112

Calculate the square root of the right side: 4.807401702

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 4.807401702 and -4.807401702.


Subproblem 1
x + 3.333333334 = 4.807401702

Simplifying
x + 3.333333334 = 4.807401702

Reorder the terms:
3.333333334 + x = 4.807401702

Solving
3.333333334 + x = 4.807401702

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 = 4.807401702 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 4.807401702 + -3.333333334
x = 4.807401702 + -3.333333334

Combine like terms: 4.807401702 + -3.333333334 = 1.474068368
x = 1.474068368

Simplifying
x = 1.474068368


Subproblem 2
x + 3.333333334 = -4.807401702

Simplifying
x + 3.333333334 = -4.807401702

Reorder the terms:
3.333333334 + x = -4.807401702

Solving
3.333333334 + x = -4.807401702

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 = -4.807401702 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -4.807401702 + -3.333333334
x = -4.807401702 + -3.333333334

Combine like terms: -4.807401702 + -3.333333334 = -8.140735036
x = -8.140735036

Simplifying
x = -8.140735036


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.474068368, -8.140735036}
Solution
x = {1.474068368, -8.140735036}

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