8x+16=(x+2)(x+5)

Solution for 8x+16=(x+2)(x+5) equation:

Simplifying
8x + 16 = (x + 2)(x + 5)

Reorder the terms:
16 + 8x = (x + 2)(x + 5)

Reorder the terms:
16 + 8x = (2 + x)(x + 5)

Reorder the terms:
16 + 8x = (2 + x)(5 + x)

Multiply (2 + x) * (5 + x)
16 + 8x = (2(5 + x) + x(5 + x))
16 + 8x = ((5 * 2 + x * 2) + x(5 + x))
16 + 8x = ((10 + 2x) + x(5 + x))
16 + 8x = (10 + 2x + (5 * x + x * x))
16 + 8x = (10 + 2x + (5x + x2))

Combine like terms: 2x + 5x = 7x
16 + 8x = (10 + 7x + x2)

Solving
16 + 8x = 10 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
16 + -10 + 8x + -7x + -1x2 = 10 + 7x + x2 + -10 + -7x + -1x2

Combine like terms: 16 + -10 = 6
6 + 8x + -7x + -1x2 = 10 + 7x + x2 + -10 + -7x + -1x2

Combine like terms: 8x + -7x = 1x
6 + 1x + -1x2 = 10 + 7x + x2 + -10 + -7x + -1x2

Reorder the terms:
6 + 1x + -1x2 = 10 + -10 + 7x + -7x + x2 + -1x2

Combine like terms: 10 + -10 = 0
6 + 1x + -1x2 = 0 + 7x + -7x + x2 + -1x2
6 + 1x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
6 + 1x + -1x2 = 0 + x2 + -1x2
6 + 1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 1x + -1x2 = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {3, -2}