3x^2-12x-210=0

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Solution for 3x^2-12x-210=0 equation: 


Simplifying
3x2 + -12x + -210 = 0

Reorder the terms:
-210 + -12x + 3x2 = 0

Solving
-210 + -12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-70 + -4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-70 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-70 + -4x + x2 = 0

Solving
-70 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -4x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -4x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -4x + x2 = 0 + 70
-4x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-4x + x2 = 70

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 70 + 4

Reorder the terms:
4 + -4x + x2 = 70 + 4

Combine like terms: 70 + 4 = 74
4 + -4x + x2 = 74

Factor a perfect square on the left side:
(x + -2)(x + -2) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + -2) equal to 8.602325267 and -8.602325267.


Subproblem 1
x + -2 = 8.602325267

Simplifying
x + -2 = 8.602325267

Reorder the terms:
-2 + x = 8.602325267

Solving
-2 + x = 8.602325267

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 8.602325267 + 2

Combine like terms: -2 + 2 = 0
0 + x = 8.602325267 + 2
x = 8.602325267 + 2

Combine like terms: 8.602325267 + 2 = 10.602325267
x = 10.602325267

Simplifying
x = 10.602325267


Subproblem 2
x + -2 = -8.602325267

Simplifying
x + -2 = -8.602325267

Reorder the terms:
-2 + x = -8.602325267

Solving
-2 + x = -8.602325267

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -8.602325267 + 2

Combine like terms: -2 + 2 = 0
0 + x = -8.602325267 + 2
x = -8.602325267 + 2

Combine like terms: -8.602325267 + 2 = -6.602325267
x = -6.602325267

Simplifying
x = -6.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.602325267, -6.602325267}
Solution
x = {10.602325267, -6.602325267}

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