x+2x(x+2x)-30=180

Solution for x+2x(x+2x)-30=180 equation:

Simplifying
x + 2x(x + 2x) + -30 = 180

Combine like terms: x + 2x = 3x
x + 2x(3x) + -30 = 180

Remove parenthesis around (3x)
x + 2x * 3x + -30 = 180

Reorder the terms for easier multiplication:
x + 2 * 3x * x + -30 = 180

Multiply 2 * 3
x + 6x * x + -30 = 180

Multiply x * x
x + 6x2 + -30 = 180

Reorder the terms:
-30 + x + 6x2 = 180

Solving
-30 + x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-30 + -180 + x + 6x2 = 180 + -180

Combine like terms: -30 + -180 = -210
-210 + x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-210 + x + 6x2 = 0

Factor a trinomial.
(-6 + -1x)(35 + -6x) = 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 '(35 + -6x)' equal to zero and attempt to solve:

Simplifying
35 + -6x = 0

Solving
35 + -6x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -6x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -6x = 0 + -35
-6x = 0 + -35

Combine like terms: 0 + -35 = -35
-6x = -35

Divide each side by '-6'.
x = 5.833333333

Simplifying
x = 5.833333333
Solution
x = {-6, 5.833333333}