5x(x-6)=180

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Solution for 5x(x-6)=180 equation: 


Simplifying
5x(x + -6) = 180

Reorder the terms:
5x(-6 + x) = 180
(-6 * 5x + x * 5x) = 180
(-30x + 5x2) = 180

Solving
-30x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -30x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + -6x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-36 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + -6x + x2 = 0

Solving
-36 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -6x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -6x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -6x + x2 = 0 + 36
-6x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-6x + x2 = 36

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 36 + 9

Reorder the terms:
9 + -6x + x2 = 36 + 9

Combine like terms: 36 + 9 = 45
9 + -6x + x2 = 45

Factor a perfect square on the left side:
(x + -3)(x + -3) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -3) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -3 = 6.708203933

Simplifying
x + -3 = 6.708203933

Reorder the terms:
-3 + x = 6.708203933

Solving
-3 + x = 6.708203933

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.708203933 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.708203933 + 3
x = 6.708203933 + 3

Combine like terms: 6.708203933 + 3 = 9.708203933
x = 9.708203933

Simplifying
x = 9.708203933


Subproblem 2
x + -3 = -6.708203933

Simplifying
x + -3 = -6.708203933

Reorder the terms:
-3 + x = -6.708203933

Solving
-3 + x = -6.708203933

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.708203933 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.708203933 + 3
x = -6.708203933 + 3

Combine like terms: -6.708203933 + 3 = -3.708203933
x = -3.708203933

Simplifying
x = -3.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.708203933, -3.708203933}
Solution
x = {9.708203933, -3.708203933}

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