0=4x^2+5x-174

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


Simplifying
0 = 4x2 + 5x + -174

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

Solving
0 = -174 + 5x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 174 = 174
174 + -5x + -4x2 = -174 + 5x + 4x2 + 174 + -5x + -4x2

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

Combine like terms: -174 + 174 = 0
174 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
174 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
174 + -5x + -4x2 = 0 + 4x2 + -4x2
174 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
174 + -5x + -4x2 = 0

Factor a trinomial.
(6 + -1x)(29 + 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 '(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
Solution
x = {6, -7.25}

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