3x(x-15)=60

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Solution for 3x(x-15)=60 equation: 


Simplifying
3x(x + -15) = 60

Reorder the terms:
3x(-15 + x) = 60
(-15 * 3x + x * 3x) = 60
(-45x + 3x2) = 60

Solving
-45x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -45x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -45x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -15x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-20 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -15x + x2 = 0

Solving
-20 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -15x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -15x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -15x + x2 = 0 + 20
-15x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-15x + x2 = 20

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 = 20 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 20 + 56.25

Combine like terms: 20 + 56.25 = 76.25
56.25 + -15x + x2 = 76.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.732124598 and -8.732124598.


Subproblem 1
x + -7.5 = 8.732124598

Simplifying
x + -7.5 = 8.732124598

Reorder the terms:
-7.5 + x = 8.732124598

Solving
-7.5 + x = 8.732124598

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 = 8.732124598 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 8.732124598 + 7.5
x = 8.732124598 + 7.5

Combine like terms: 8.732124598 + 7.5 = 16.232124598
x = 16.232124598

Simplifying
x = 16.232124598


Subproblem 2
x + -7.5 = -8.732124598

Simplifying
x + -7.5 = -8.732124598

Reorder the terms:
-7.5 + x = -8.732124598

Solving
-7.5 + x = -8.732124598

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 = -8.732124598 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -8.732124598 + 7.5
x = -8.732124598 + 7.5

Combine like terms: -8.732124598 + 7.5 = -1.232124598
x = -1.232124598

Simplifying
x = -1.232124598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.232124598, -1.232124598}
Solution
x = {16.232124598, -1.232124598}

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