3x(2x+50)=180

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Solution for 3x(2x+50)=180 equation: 


Simplifying
3x(2x + 50) = 180

Reorder the terms:
3x(50 + 2x) = 180
(50 * 3x + 2x * 3x) = 180
(150x + 6x2) = 180

Solving
150x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 150x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 150x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 25x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 25x + x2 = 0

Solving
-30 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 25x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 25x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 25x + x2 = 0 + 30
25x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
25x + x2 = 30

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 30 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 30 + 156.25

Combine like terms: 30 + 156.25 = 186.25
156.25 + 25x + x2 = 186.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.647344064 and -13.647344064.


Subproblem 1
x + 12.5 = 13.647344064

Simplifying
x + 12.5 = 13.647344064

Reorder the terms:
12.5 + x = 13.647344064

Solving
12.5 + x = 13.647344064

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 13.647344064 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 13.647344064 + -12.5
x = 13.647344064 + -12.5

Combine like terms: 13.647344064 + -12.5 = 1.147344064
x = 1.147344064

Simplifying
x = 1.147344064


Subproblem 2
x + 12.5 = -13.647344064

Simplifying
x + 12.5 = -13.647344064

Reorder the terms:
12.5 + x = -13.647344064

Solving
12.5 + x = -13.647344064

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -13.647344064 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -13.647344064 + -12.5
x = -13.647344064 + -12.5

Combine like terms: -13.647344064 + -12.5 = -26.147344064
x = -26.147344064

Simplifying
x = -26.147344064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.147344064, -26.147344064}
Solution
x = {1.147344064, -26.147344064}

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