360=(3x+5)(2x+8)

Solution for 360=(3x+5)(2x+8) equation:

Simplifying
360 = (3x + 5)(2x + 8)

Reorder the terms:
360 = (5 + 3x)(2x + 8)

Reorder the terms:
360 = (5 + 3x)(8 + 2x)

Multiply (5 + 3x) * (8 + 2x)
360 = (5(8 + 2x) + 3x * (8 + 2x))
360 = ((8 * 5 + 2x * 5) + 3x * (8 + 2x))
360 = ((40 + 10x) + 3x * (8 + 2x))
360 = (40 + 10x + (8 * 3x + 2x * 3x))
360 = (40 + 10x + (24x + 6x2))

Combine like terms: 10x + 24x = 34x
360 = (40 + 34x + 6x2)

Solving
360 = 40 + 34x + 6x2

Solving for variable 'x'.

Combine like terms: 360 + -40 = 320
320 + -34x + -6x2 = 40 + 34x + 6x2 + -40 + -34x + -6x2

Reorder the terms:
320 + -34x + -6x2 = 40 + -40 + 34x + -34x + 6x2 + -6x2

Combine like terms: 40 + -40 = 0
320 + -34x + -6x2 = 0 + 34x + -34x + 6x2 + -6x2
320 + -34x + -6x2 = 34x + -34x + 6x2 + -6x2

Combine like terms: 34x + -34x = 0
320 + -34x + -6x2 = 0 + 6x2 + -6x2
320 + -34x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
320 + -34x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(160 + -17x + -3x2) = 0

Factor a trinomial.
2((5 + -1x)(32 + 3x)) = 0

Ignore the factor 2.
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 '(32 + 3x)' equal to zero and attempt to solve:

Simplifying
32 + 3x = 0

Solving
32 + 3x = 0

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

Add '-32' to each side of the equation.
32 + -32 + 3x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 3x = 0 + -32
3x = 0 + -32

Combine like terms: 0 + -32 = -32
3x = -32

Divide each side by '3'.
x = -10.66666667

Simplifying
x = -10.66666667
Solution
x = {5, -10.66666667}