0=x^2+29x+54

Solution for 0=x^2+29x+54 equation:

Simplifying
0 = x2 + 29x + 54

Reorder the terms:
0 = 54 + 29x + x2

Solving
0 = 54 + 29x + x2

Solving for variable 'x'.

Combine like terms: 0 + -54 = -54
-54 + -29x + -1x2 = 54 + 29x + x2 + -54 + -29x + -1x2

Reorder the terms:
-54 + -29x + -1x2 = 54 + -54 + 29x + -29x + x2 + -1x2

Combine like terms: 54 + -54 = 0
-54 + -29x + -1x2 = 0 + 29x + -29x + x2 + -1x2
-54 + -29x + -1x2 = 29x + -29x + x2 + -1x2

Combine like terms: 29x + -29x = 0
-54 + -29x + -1x2 = 0 + x2 + -1x2
-54 + -29x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-54 + -29x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(54 + 29x + x2) = 0

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

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

Simplifying
27 + x = 0

Solving
27 + x = 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 + x = 0 + -27

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-27, -2}