2x(x-33)+x=33

Solution for 2x(x-33)+x=33 equation:

Simplifying
2x(x + -33) + x = 33

Reorder the terms:
2x(-33 + x) + x = 33
(-33 * 2x + x * 2x) + x = 33
(-66x + 2x2) + x = 33

Reorder the terms:
-66x + x + 2x2 = 33

Combine like terms: -66x + x = -65x
-65x + 2x2 = 33

Solving
-65x + 2x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + -65x + 2x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -65x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(33 + -1x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve:

Simplifying
33 + -1x = 0

Solving
33 + -1x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -1x = 0 + -33

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

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

Divide each side by '-1'.
x = 33

Simplifying
x = 33
Solution
x = {-0.5, 33}