2x(x-30)=180

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Solution for 2x(x-30)=180 equation: 


Simplifying
2x(x + -30) = 180

Reorder the terms:
2x(-30 + x) = 180
(-30 * 2x + x * 2x) = 180
(-60x + 2x2) = 180

Solving
-60x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -60x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -60x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + -30x + x2 = 0

Solving
-90 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -30x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -30x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -30x + x2 = 0 + 90
-30x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-30x + x2 = 90

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 90 + 225

Reorder the terms:
225 + -30x + x2 = 90 + 225

Combine like terms: 90 + 225 = 315
225 + -30x + x2 = 315

Factor a perfect square on the left side:
(x + -15)(x + -15) = 315

Calculate the square root of the right side: 17.748239349

Break this problem into two subproblems by setting 
(x + -15) equal to 17.748239349 and -17.748239349.


Subproblem 1
x + -15 = 17.748239349

Simplifying
x + -15 = 17.748239349

Reorder the terms:
-15 + x = 17.748239349

Solving
-15 + x = 17.748239349

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 17.748239349 + 15

Combine like terms: -15 + 15 = 0
0 + x = 17.748239349 + 15
x = 17.748239349 + 15

Combine like terms: 17.748239349 + 15 = 32.748239349
x = 32.748239349

Simplifying
x = 32.748239349


Subproblem 2
x + -15 = -17.748239349

Simplifying
x + -15 = -17.748239349

Reorder the terms:
-15 + x = -17.748239349

Solving
-15 + x = -17.748239349

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -17.748239349 + 15

Combine like terms: -15 + 15 = 0
0 + x = -17.748239349 + 15
x = -17.748239349 + 15

Combine like terms: -17.748239349 + 15 = -2.748239349
x = -2.748239349

Simplifying
x = -2.748239349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.748239349, -2.748239349}
Solution
x = {32.748239349, -2.748239349}

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