7x(3x+20)=180

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Solution for 7x(3x+20)=180 equation: 


Simplifying
7x(3x + 20) = 180

Reorder the terms:
7x(20 + 3x) = 180
(20 * 7x + 3x * 7x) = 180
(140x + 21x2) = 180

Solving
140x + 21x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 140x + 21x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 140x + 21x2 = 0

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

Divide each side by '21'.
-8.571428571 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + 6.666666667x + 8.571428571 + x2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + 6.666666667x + x2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + 8.571428571
6.666666667x + x2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
6.666666667x + x2 = 8.571428571

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 = 8.571428571 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 8.571428571 + 11.11111112

Combine like terms: 8.571428571 + 11.11111112 = 19.682539691
11.11111112 + 6.666666667x + x2 = 19.682539691

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 19.682539691

Calculate the square root of the right side: 4.436500839

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 4.436500839 and -4.436500839.


Subproblem 1
x + 3.333333334 = 4.436500839

Simplifying
x + 3.333333334 = 4.436500839

Reorder the terms:
3.333333334 + x = 4.436500839

Solving
3.333333334 + x = 4.436500839

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 = 4.436500839 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 4.436500839 + -3.333333334
x = 4.436500839 + -3.333333334

Combine like terms: 4.436500839 + -3.333333334 = 1.103167505
x = 1.103167505

Simplifying
x = 1.103167505


Subproblem 2
x + 3.333333334 = -4.436500839

Simplifying
x + 3.333333334 = -4.436500839

Reorder the terms:
3.333333334 + x = -4.436500839

Solving
3.333333334 + x = -4.436500839

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 = -4.436500839 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -4.436500839 + -3.333333334
x = -4.436500839 + -3.333333334

Combine like terms: -4.436500839 + -3.333333334 = -7.769834173
x = -7.769834173

Simplifying
x = -7.769834173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.103167505, -7.769834173}

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