4x^2+5x-174=0

Solution for 4x^2+5x-174=0 equation:

Simplifying
4x2 + 5x + -174 = 0

Reorder the terms:
-174 + 5x + 4x2 = 0

Solving
-174 + 5x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-29 + -4x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-29 + -4x)' equal to zero and attempt to solve:

Simplifying
-29 + -4x = 0

Solving
-29 + -4x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -4x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -4x = 0 + 29
-4x = 0 + 29

Combine like terms: 0 + 29 = 29
-4x = 29

Divide each side by '-4'.
x = -7.25

Simplifying
x = -7.25
Subproblem 2
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
Solution
x = {-7.25, 6}