0=4x^2-31x-90

Solution for 0=4x^2-31x-90 equation:

Simplifying
0 = 4x2 + -31x + -90

Reorder the terms:
0 = -90 + -31x + 4x2

Solving
0 = -90 + -31x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 90 = 90
90 + 31x + -4x2 = -90 + -31x + 4x2 + 90 + 31x + -4x2

Reorder the terms:
90 + 31x + -4x2 = -90 + 90 + -31x + 31x + 4x2 + -4x2

Combine like terms: -90 + 90 = 0
90 + 31x + -4x2 = 0 + -31x + 31x + 4x2 + -4x2
90 + 31x + -4x2 = -31x + 31x + 4x2 + -4x2

Combine like terms: -31x + 31x = 0
90 + 31x + -4x2 = 0 + 4x2 + -4x2
90 + 31x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
90 + 31x + -4x2 = 0

Factor a trinomial.
(10 + -1x)(9 + 4x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
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
Solution
x = {10, -2.25}