(2x+8)(x+3)=84

Solution for (2x+8)(x+3)=84 equation:

Simplifying
(2x + 8)(x + 3) = 84

Reorder the terms:
(8 + 2x)(x + 3) = 84

Reorder the terms:
(8 + 2x)(3 + x) = 84

Multiply (8 + 2x) * (3 + x)
(8(3 + x) + 2x * (3 + x)) = 84
((3 * 8 + x * 8) + 2x * (3 + x)) = 84
((24 + 8x) + 2x * (3 + x)) = 84
(24 + 8x + (3 * 2x + x * 2x)) = 84
(24 + 8x + (6x + 2x2)) = 84

Combine like terms: 8x + 6x = 14x
(24 + 14x + 2x2) = 84

Solving
24 + 14x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
24 + -84 + 14x + 2x2 = 84 + -84

Combine like terms: 24 + -84 = -60
-60 + 14x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-60 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 7x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
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 = {-10, 3}