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

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


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

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

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

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

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

Solving
40 + 34x + 6x2 = 360

Solving for variable 'x'.

Reorder the terms:
40 + -360 + 34x + 6x2 = 360 + -360

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

Combine like terms: 360 + -360 = 0
-320 + 34x + 6x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-10.66666667, 5}

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