0=3x^2+21x-54

Solution for 0=3x^2+21x-54 equation:

Simplifying
0 = 3x2 + 21x + -54

Reorder the terms:
0 = -54 + 21x + 3x2

Solving
0 = -54 + 21x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -21x + -3x2 = -54 + 21x + 3x2 + 54 + -21x + -3x2

Reorder the terms:
54 + -21x + -3x2 = -54 + 54 + 21x + -21x + 3x2 + -3x2

Combine like terms: -54 + 54 = 0
54 + -21x + -3x2 = 0 + 21x + -21x + 3x2 + -3x2
54 + -21x + -3x2 = 21x + -21x + 3x2 + -3x2

Combine like terms: 21x + -21x = 0
54 + -21x + -3x2 = 0 + 3x2 + -3x2
54 + -21x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
54 + -21x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -7x + -1x2) = 0

Factor a trinomial.
3((2 + -1x)(9 + x)) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {2, -9}