3x^2+54x-57=0

Solution for 3x^2+54x-57=0 equation:

Simplifying
3x2 + 54x + -57 = 0

Reorder the terms:
-57 + 54x + 3x2 = 0

Solving
-57 + 54x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + 18x + x2) = 0

Factor a trinomial.
3((-19 + -1x)(1 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19
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 = {-19, 1}