7x^2+38x+51=0

Solution for 7x^2+38x+51=0 equation:

Simplifying
7x2 + 38x + 51 = 0

Reorder the terms:
51 + 38x + 7x2 = 0

Solving
51 + 38x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(17 + 7x) = 0

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(17 + 7x)' equal to zero and attempt to solve:

Simplifying
17 + 7x = 0

Solving
17 + 7x = 0

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

Add '-17' to each side of the equation.
17 + -17 + 7x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 7x = 0 + -17
7x = 0 + -17

Combine like terms: 0 + -17 = -17
7x = -17

Divide each side by '7'.
x = -2.428571429

Simplifying
x = -2.428571429
Solution
x = {-3, -2.428571429}