30=.5(2x+2)(x)

Solution for 30=.5(2x+2)(x) equation:

Simplifying
30 = 0.5(2x + 2)(x)

Reorder the terms:
30 = 0.5(2 + 2x)(x)

Reorder the terms for easier multiplication:
30 = 0.5x(2 + 2x)
30 = (2 * 0.5x + 2x * 0.5x)
30 = (1x + 1x2)

Solving
30 = 1x + 1x2

Solving for variable 'x'.

Reorder the terms:
30 + -1x + -1x2 = 1x + -1x + 1x2 + -1x2

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

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

Factor a trinomial.
(5 + -1x)(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {5, -6}