4x^2-23x+6=78

Solution for 4x^2-23x+6=78 equation:

Simplifying
4x2 + -23x + 6 = 78

Reorder the terms:
6 + -23x + 4x2 = 78

Solving
6 + -23x + 4x2 = 78

Solving for variable 'x'.

Reorder the terms:
6 + -78 + -23x + 4x2 = 78 + -78

Combine like terms: 6 + -78 = -72
-72 + -23x + 4x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-72 + -23x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 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 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2.25, 8}