0=4x^2-11x-78

Solution for 0=4x^2-11x-78 equation:

Simplifying
0 = 4x2 + -11x + -78

Reorder the terms:
0 = -78 + -11x + 4x2

Solving
0 = -78 + -11x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 78 = 78
78 + 11x + -4x2 = -78 + -11x + 4x2 + 78 + 11x + -4x2

Reorder the terms:
78 + 11x + -4x2 = -78 + 78 + -11x + 11x + 4x2 + -4x2

Combine like terms: -78 + 78 = 0
78 + 11x + -4x2 = 0 + -11x + 11x + 4x2 + -4x2
78 + 11x + -4x2 = -11x + 11x + 4x2 + -4x2

Combine like terms: -11x + 11x = 0
78 + 11x + -4x2 = 0 + 4x2 + -4x2
78 + 11x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
78 + 11x + -4x2 = 0

Factor a trinomial.
(6 + -1x)(13 + 4x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(13 + 4x)' equal to zero and attempt to solve:

Simplifying
13 + 4x = 0

Solving
13 + 4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 4x = 0 + -13
4x = 0 + -13

Combine like terms: 0 + -13 = -13
4x = -13

Divide each side by '4'.
x = -3.25

Simplifying
x = -3.25
Solution
x = {6, -3.25}