3x^2+60x-225=0

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Solution for 3x^2+60x-225=0 equation: 


Simplifying
3x2 + 60x + -225 = 0

Reorder the terms:
-225 + 60x + 3x2 = 0

Solving
-225 + 60x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-75 + 20x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-75 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + 20x + x2 = 0

Solving
-75 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 20x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 20x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 20x + x2 = 0 + 75
20x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
20x + x2 = 75

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 75 + 100

Reorder the terms:
100 + 20x + x2 = 75 + 100

Combine like terms: 75 + 100 = 175
100 + 20x + x2 = 175

Factor a perfect square on the left side:
(x + 10)(x + 10) = 175

Calculate the square root of the right side: 13.228756555

Break this problem into two subproblems by setting 
(x + 10) equal to 13.228756555 and -13.228756555.


Subproblem 1
x + 10 = 13.228756555

Simplifying
x + 10 = 13.228756555

Reorder the terms:
10 + x = 13.228756555

Solving
10 + x = 13.228756555

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 13.228756555 + -10

Combine like terms: 10 + -10 = 0
0 + x = 13.228756555 + -10
x = 13.228756555 + -10

Combine like terms: 13.228756555 + -10 = 3.228756555
x = 3.228756555

Simplifying
x = 3.228756555


Subproblem 2
x + 10 = -13.228756555

Simplifying
x + 10 = -13.228756555

Reorder the terms:
10 + x = -13.228756555

Solving
10 + x = -13.228756555

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -13.228756555 + -10

Combine like terms: 10 + -10 = 0
0 + x = -13.228756555 + -10
x = -13.228756555 + -10

Combine like terms: -13.228756555 + -10 = -23.228756555
x = -23.228756555

Simplifying
x = -23.228756555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.228756555, -23.228756555}
Solution
x = {3.228756555, -23.228756555}

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