7x^2+51x+54=0

Solution for 7x^2+51x+54=0 equation:

Simplifying
7x2 + 51x + 54 = 0

Reorder the terms:
54 + 51x + 7x2 = 0

Solving
54 + 51x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(9 + 7x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(9 + 7x)' equal to zero and attempt to solve:

Simplifying
9 + 7x = 0

Solving
9 + 7x = 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 + 7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7x = 0 + -9
7x = 0 + -9

Combine like terms: 0 + -9 = -9
7x = -9

Divide each side by '7'.
x = -1.285714286

Simplifying
x = -1.285714286
Solution
x = {-6, -1.285714286}