x(x+1)+3=33

Solution for x(x+1)+3=33 equation:

Simplifying
x(x + 1) + 3 = 33

Reorder the terms:
x(1 + x) + 3 = 33
(1 * x + x * x) + 3 = 33
(1x + x2) + 3 = 33

Reorder the terms:
3 + 1x + x2 = 33

Solving
3 + 1x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
3 + -33 + 1x + x2 = 33 + -33

Combine like terms: 3 + -33 = -30
-30 + 1x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-30 + 1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 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 '(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
Solution
x = {-6, 5}