(2x+8)(x)=42

Solution for (2x+8)(x)=42 equation:

Simplifying
(2x + 8)(x) = 42

Reorder the terms:
(8 + 2x)(x) = 42

Reorder the terms for easier multiplication:
x(8 + 2x) = 42
(8 * x + 2x * x) = 42
(8x + 2x2) = 42

Solving
8x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 8x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 4x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}