x^2+4x=1020

Solution for x^2+4x=1020 equation:

Simplifying
x2 + 4x = 1020

Reorder the terms:
4x + x2 = 1020

Solving
4x + x2 = 1020

Solving for variable 'x'.

Reorder the terms:
-1020 + 4x + x2 = 1020 + -1020

Combine like terms: 1020 + -1020 = 0
-1020 + 4x + x2 = 0

Factor a trinomial.
(-34 + -1x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-34, 30}