2x^2+52x-54=0

Solution for 2x^2+52x-54=0 equation:

Simplifying
2x2 + 52x + -54 = 0

Reorder the terms:
-54 + 52x + 2x2 = 0

Solving
-54 + 52x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 26x + x2) = 0

Factor a trinomial.
2((-27 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-27, 1}