(2x)x+(6)x-780=0

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Solution for (2x)x+(6)x-780=0 equation: 


Simplifying
(2x) * x + (6) * x + -780 = 0

Remove parenthesis around (2x)
2x * x + (6) * x + -780 = 0

Multiply x * x
2x2 + (6) * x + -780 = 0

Reorder the terms:
-780 + 6x + 2x2 = 0

Solving
-780 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-390 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-390 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-390 + 3x + x2 = 0

Solving
-390 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '390' to each side of the equation.
-390 + 3x + 390 + x2 = 0 + 390

Reorder the terms:
-390 + 390 + 3x + x2 = 0 + 390

Combine like terms: -390 + 390 = 0
0 + 3x + x2 = 0 + 390
3x + x2 = 0 + 390

Combine like terms: 0 + 390 = 390
3x + x2 = 390

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 390 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 390 + 2.25

Combine like terms: 390 + 2.25 = 392.25
2.25 + 3x + x2 = 392.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 392.25

Calculate the square root of the right side: 19.80530232

Break this problem into two subproblems by setting 
(x + 1.5) equal to 19.80530232 and -19.80530232.


Subproblem 1
x + 1.5 = 19.80530232

Simplifying
x + 1.5 = 19.80530232

Reorder the terms:
1.5 + x = 19.80530232

Solving
1.5 + x = 19.80530232

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 19.80530232 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 19.80530232 + -1.5
x = 19.80530232 + -1.5

Combine like terms: 19.80530232 + -1.5 = 18.30530232
x = 18.30530232

Simplifying
x = 18.30530232


Subproblem 2
x + 1.5 = -19.80530232

Simplifying
x + 1.5 = -19.80530232

Reorder the terms:
1.5 + x = -19.80530232

Solving
1.5 + x = -19.80530232

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -19.80530232 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -19.80530232 + -1.5
x = -19.80530232 + -1.5

Combine like terms: -19.80530232 + -1.5 = -21.30530232
x = -21.30530232

Simplifying
x = -21.30530232


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.30530232, -21.30530232}
Solution
x = {18.30530232, -21.30530232}

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