3x(2x+50)=30

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Solution for 3x(2x+50)=30 equation: 


Simplifying
3x(2x + 50) = 30

Reorder the terms:
3x(50 + 2x) = 30
(50 * 3x + 2x * 3x) = 30
(150x + 6x2) = 30

Solving
150x + 6x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 150x + 6x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 150x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 25x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-5 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 25x + x2 = 0

Solving
-5 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 25x + x2 = 0 + 5
25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
25x + x2 = 5

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 = 5 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 5 + 156.25

Combine like terms: 5 + 156.25 = 161.25
156.25 + 25x + x2 = 161.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 161.25

Calculate the square root of the right side: 12.698425099

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.698425099 and -12.698425099.


Subproblem 1
x + 12.5 = 12.698425099

Simplifying
x + 12.5 = 12.698425099

Reorder the terms:
12.5 + x = 12.698425099

Solving
12.5 + x = 12.698425099

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 = 12.698425099 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.698425099 + -12.5
x = 12.698425099 + -12.5

Combine like terms: 12.698425099 + -12.5 = 0.198425099
x = 0.198425099

Simplifying
x = 0.198425099


Subproblem 2
x + 12.5 = -12.698425099

Simplifying
x + 12.5 = -12.698425099

Reorder the terms:
12.5 + x = -12.698425099

Solving
12.5 + x = -12.698425099

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 = -12.698425099 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.698425099 + -12.5
x = -12.698425099 + -12.5

Combine like terms: -12.698425099 + -12.5 = -25.198425099
x = -25.198425099

Simplifying
x = -25.198425099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.198425099, -25.198425099}
Solution
x = {0.198425099, -25.198425099}

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