(5x^2-20)+(31x-4)-180=0

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Solution for (5x^2-20)+(31x-4)-180=0 equation: 


Simplifying
(5x2 + -20) + (31x + -4) + -180 = 0

Reorder the terms:
(-20 + 5x2) + (31x + -4) + -180 = 0

Remove parenthesis around (-20 + 5x2)
-20 + 5x2 + (31x + -4) + -180 = 0

Reorder the terms:
-20 + 5x2 + (-4 + 31x) + -180 = 0

Remove parenthesis around (-4 + 31x)
-20 + 5x2 + -4 + 31x + -180 = 0

Reorder the terms:
-20 + -4 + -180 + 31x + 5x2 = 0

Combine like terms: -20 + -4 = -24
-24 + -180 + 31x + 5x2 = 0

Combine like terms: -24 + -180 = -204
-204 + 31x + 5x2 = 0

Solving
-204 + 31x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-51 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-51 + -5x)' equal to zero and attempt to solve:

Simplifying
-51 + -5x = 0

Solving
-51 + -5x = 0

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

Add '51' to each side of the equation.
-51 + 51 + -5x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -5x = 0 + 51
-5x = 0 + 51

Combine like terms: 0 + 51 = 51
-5x = 51

Divide each side by '-5'.
x = -10.2

Simplifying
x = -10.2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-10.2, 4}

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