(1+2x)(x)=66

Solution for (1+2x)(x)=66 equation:

Simplifying
(1 + 2x)(x) = 66

Reorder the terms for easier multiplication:
x(1 + 2x) = 66
(1 * x + 2x * x) = 66
(1x + 2x2) = 66

Solving
1x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + 1x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 1x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(11 + -2x) = 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 '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 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 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-6, 5.5}