(x*x)+2x+5=20

Solution for (x*x)+2x+5=20 equation:

Simplifying
(x * x) + 2x + 5 = 20

Multiply x * x
(x2) + 2x + 5 = 20
x2 + 2x + 5 = 20

Reorder the terms:
5 + 2x + x2 = 20

Solving
5 + 2x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
5 + -20 + 2x + x2 = 20 + -20

Combine like terms: 5 + -20 = -15
-15 + 2x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-15 + 2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -1x) = 0

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5, 3}