4x(x-15)=180

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Solution for 4x(x-15)=180 equation: 


Simplifying
4x(x + -15) = 180

Reorder the terms:
4x(-15 + x) = 180
(-15 * 4x + x * 4x) = 180
(-60x + 4x2) = 180

Solving
-60x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -60x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + -15x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + -15x + x2 = 0

Solving
-45 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -15x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -15x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -15x + x2 = 0 + 45
-15x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-15x + x2 = 45

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 45 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 45 + 56.25

Combine like terms: 45 + 56.25 = 101.25
56.25 + -15x + x2 = 101.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + -7.5) equal to 10.062305899 and -10.062305899.


Subproblem 1
x + -7.5 = 10.062305899

Simplifying
x + -7.5 = 10.062305899

Reorder the terms:
-7.5 + x = 10.062305899

Solving
-7.5 + x = 10.062305899

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 10.062305899 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 10.062305899 + 7.5
x = 10.062305899 + 7.5

Combine like terms: 10.062305899 + 7.5 = 17.562305899
x = 17.562305899

Simplifying
x = 17.562305899


Subproblem 2
x + -7.5 = -10.062305899

Simplifying
x + -7.5 = -10.062305899

Reorder the terms:
-7.5 + x = -10.062305899

Solving
-7.5 + x = -10.062305899

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -10.062305899 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -10.062305899 + 7.5
x = -10.062305899 + 7.5

Combine like terms: -10.062305899 + 7.5 = -2.562305899
x = -2.562305899

Simplifying
x = -2.562305899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.562305899, -2.562305899}
Solution
x = {17.562305899, -2.562305899}

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