X^2+4X=77

Solution for X^2+4X=77 equation:

Simplifying
X2 + 4X = 77

Reorder the terms:
4X + X2 = 77

Solving
4X + X2 = 77

Solving for variable 'X'.

Reorder the terms:
-77 + 4X + X2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 4X + X2 = 0

Factor a trinomial.
(-11 + -1X)(7 + -1X) = 0

Subproblem 1
Set the factor '(-11 + -1X)' equal to zero and attempt to solve:

Simplifying
-11 + -1X = 0

Solving
-11 + -1X = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1X = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1X = 0 + 11
-1X = 0 + 11

Combine like terms: 0 + 11 = 11
-1X = 11

Divide each side by '-1'.
X = -11

Simplifying
X = -11
Subproblem 2
Set the factor '(7 + -1X)' equal to zero and attempt to solve:

Simplifying
7 + -1X = 0

Solving
7 + -1X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1X = 0 + -7
-1X = 0 + -7

Combine like terms: 0 + -7 = -7
-1X = -7

Divide each side by '-1'.
X = 7

Simplifying
X = 7
Solution
X = {-11, 7}