x^2+78x-243=0

Solution for x^2+78x-243=0 equation:

Simplifying
x2 + 78x + -243 = 0

Reorder the terms:
-243 + 78x + x2 = 0

Solving
-243 + 78x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-81 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-81 + -1x)' equal to zero and attempt to solve:

Simplifying
-81 + -1x = 0

Solving
-81 + -1x = 0

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

Add '81' to each side of the equation.
-81 + 81 + -1x = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -1x = 0 + 81
-1x = 0 + 81

Combine like terms: 0 + 81 = 81
-1x = 81

Divide each side by '-1'.
x = -81

Simplifying
x = -81
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-81, 3}