2x^2+3x-54-x^2=0

Solution for 2x^2+3x-54-x^2=0 equation:

Simplifying
2x2 + 3x + -54 + -1x2 = 0

Reorder the terms:
-54 + 3x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-54 + 3x + 1x2 = 0

Solving
-54 + 3x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-9, 6}