4x^2+840x-43200=0

Solution for 4x^2+840x-43200=0 equation:

Simplifying
4x2 + 840x + -43200 = 0

Reorder the terms:
-43200 + 840x + 4x2 = 0

Solving
-43200 + 840x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10800 + 210x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-10800 + 210x + x2)' equal to zero and attempt to solve:

Simplifying
-10800 + 210x + x2 = 0

Solving
-10800 + 210x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10800' to each side of the equation.
-10800 + 210x + 10800 + x2 = 0 + 10800

Reorder the terms:
-10800 + 10800 + 210x + x2 = 0 + 10800

Combine like terms: -10800 + 10800 = 0
0 + 210x + x2 = 0 + 10800
210x + x2 = 0 + 10800

Combine like terms: 0 + 10800 = 10800
210x + x2 = 10800

The x term is 210x.  Take half its coefficient (105).
Square it (11025) and add it to both sides.

Add '11025' to each side of the equation.
210x + 11025 + x2 = 10800 + 11025

Reorder the terms:
11025 + 210x + x2 = 10800 + 11025

Combine like terms: 10800 + 11025 = 21825
11025 + 210x + x2 = 21825

Factor a perfect square on the left side:
(x + 105)(x + 105) = 21825

Calculate the square root of the right side: 147.732867027

Break this problem into two subproblems by setting 
(x + 105) equal to 147.732867027 and -147.732867027.

Subproblem 1
x + 105 = 147.732867027

Simplifying
x + 105 = 147.732867027

Reorder the terms:
105 + x = 147.732867027

Solving
105 + x = 147.732867027

Solving for variable 'x'.

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

Add '-105' to each side of the equation.
105 + -105 + x = 147.732867027 + -105

Combine like terms: 105 + -105 = 0
0 + x = 147.732867027 + -105
x = 147.732867027 + -105

Combine like terms: 147.732867027 + -105 = 42.732867027
x = 42.732867027

Simplifying
x = 42.732867027

Subproblem 2
x + 105 = -147.732867027

Simplifying
x + 105 = -147.732867027

Reorder the terms:
105 + x = -147.732867027

Solving
105 + x = -147.732867027

Solving for variable 'x'.

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

Add '-105' to each side of the equation.
105 + -105 + x = -147.732867027 + -105

Combine like terms: 105 + -105 = 0
0 + x = -147.732867027 + -105
x = -147.732867027 + -105

Combine like terms: -147.732867027 + -105 = -252.732867027
x = -252.732867027

Simplifying
x = -252.732867027

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.732867027, -252.732867027}
Solution
x = {42.732867027, -252.732867027}