5x^2-21x=-22

Solution for 5x^2-21x=-22 equation:

Simplifying
5x2 + -21x = -22

Reorder the terms:
-21x + 5x2 = -22

Solving
-21x + 5x2 = -22

Solving for variable 'x'.

Reorder the terms:
22 + -21x + 5x2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -21x + 5x2 = 0

Factor a trinomial.
(2 + -1x)(11 + -5x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(11 + -5x)' equal to zero and attempt to solve:

Simplifying
11 + -5x = 0

Solving
11 + -5x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x = 0 + -11
-5x = 0 + -11

Combine like terms: 0 + -11 = -11
-5x = -11

Divide each side by '-5'.
x = 2.2

Simplifying
x = 2.2
Solution
x = {2, 2.2}