4x^2+47x+78=0

Solution for 4x^2+47x+78=0 equation:

Simplifying
4x2 + 47x + 78 = 0

Reorder the terms:
78 + 47x + 4x2 = 0

Solving
78 + 47x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(39 + 4x)(2 + x) = 0

Subproblem 1
Set the factor '(39 + 4x)' equal to zero and attempt to solve:

Simplifying
39 + 4x = 0

Solving
39 + 4x = 0

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

Add '-39' to each side of the equation.
39 + -39 + 4x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 4x = 0 + -39
4x = 0 + -39

Combine like terms: 0 + -39 = -39
4x = -39

Divide each side by '4'.
x = -9.75

Simplifying
x = -9.75
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 = {-9.75, -2}