4x^2+29x+51=0

Solution for 4x^2+29x+51=0 equation:

Simplifying
4x2 + 29x + 51 = 0

Reorder the terms:
51 + 29x + 4x2 = 0

Solving
51 + 29x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(17 + 4x)(3 + x) = 0

Subproblem 1
Set the factor '(17 + 4x)' equal to zero and attempt to solve:

Simplifying
17 + 4x = 0

Solving
17 + 4x = 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 + 4x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 4x = 0 + -17
4x = 0 + -17

Combine like terms: 0 + -17 = -17
4x = -17

Divide each side by '4'.
x = -4.25

Simplifying
x = -4.25
Subproblem 2
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
Solution
x = {-4.25, -3}