3x(2x+20)=180

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Solution for 3x(2x+20)=180 equation: 


Simplifying
3x(2x + 20) = 180

Reorder the terms:
3x(20 + 2x) = 180
(20 * 3x + 2x * 3x) = 180
(60x + 6x2) = 180

Solving
60x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 60x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 60x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 10x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 10x + x2 = 0

Solving
-30 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 10x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 10x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 10x + x2 = 0 + 30
10x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
10x + x2 = 30

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 30 + 25

Reorder the terms:
25 + 10x + x2 = 30 + 25

Combine like terms: 30 + 25 = 55
25 + 10x + x2 = 55

Factor a perfect square on the left side:
(x + 5)(x + 5) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 5) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + 5 = 7.416198487

Simplifying
x + 5 = 7.416198487

Reorder the terms:
5 + x = 7.416198487

Solving
5 + x = 7.416198487

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + x = 7.416198487 + -5
x = 7.416198487 + -5

Combine like terms: 7.416198487 + -5 = 2.416198487
x = 2.416198487

Simplifying
x = 2.416198487


Subproblem 2
x + 5 = -7.416198487

Simplifying
x + 5 = -7.416198487

Reorder the terms:
5 + x = -7.416198487

Solving
5 + x = -7.416198487

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + x = -7.416198487 + -5
x = -7.416198487 + -5

Combine like terms: -7.416198487 + -5 = -12.416198487
x = -12.416198487

Simplifying
x = -12.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.416198487, -12.416198487}
Solution
x = {2.416198487, -12.416198487}

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