(x+8)(x+5)=(3x-5)(x-8)

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


Simplifying
(x + 8)(x + 5) = (3x + -5)(x + -8)

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

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

Multiply (8 + x) * (5 + x)
(8(5 + x) + x(5 + x)) = (3x + -5)(x + -8)
((5 * 8 + x * 8) + x(5 + x)) = (3x + -5)(x + -8)
((40 + 8x) + x(5 + x)) = (3x + -5)(x + -8)
(40 + 8x + (5 * x + x * x)) = (3x + -5)(x + -8)
(40 + 8x + (5x + x2)) = (3x + -5)(x + -8)

Combine like terms: 8x + 5x = 13x
(40 + 13x + x2) = (3x + -5)(x + -8)

Reorder the terms:
40 + 13x + x2 = (-5 + 3x)(x + -8)

Reorder the terms:
40 + 13x + x2 = (-5 + 3x)(-8 + x)

Multiply (-5 + 3x) * (-8 + x)
40 + 13x + x2 = (-5(-8 + x) + 3x * (-8 + x))
40 + 13x + x2 = ((-8 * -5 + x * -5) + 3x * (-8 + x))
40 + 13x + x2 = ((40 + -5x) + 3x * (-8 + x))
40 + 13x + x2 = (40 + -5x + (-8 * 3x + x * 3x))
40 + 13x + x2 = (40 + -5x + (-24x + 3x2))

Combine like terms: -5x + -24x = -29x
40 + 13x + x2 = (40 + -29x + 3x2)

Add '-40' to each side of the equation.
40 + 13x + -40 + x2 = 40 + -29x + -40 + 3x2

Reorder the terms:
40 + -40 + 13x + x2 = 40 + -29x + -40 + 3x2

Combine like terms: 40 + -40 = 0
0 + 13x + x2 = 40 + -29x + -40 + 3x2
13x + x2 = 40 + -29x + -40 + 3x2

Reorder the terms:
13x + x2 = 40 + -40 + -29x + 3x2

Combine like terms: 40 + -40 = 0
13x + x2 = 0 + -29x + 3x2
13x + x2 = -29x + 3x2

Solving
13x + x2 = -29x + 3x2

Solving for variable 'x'.

Reorder the terms:
13x + 29x + x2 + -3x2 = -29x + 3x2 + 29x + -3x2

Combine like terms: 13x + 29x = 42x
42x + x2 + -3x2 = -29x + 3x2 + 29x + -3x2

Combine like terms: x2 + -3x2 = -2x2
42x + -2x2 = -29x + 3x2 + 29x + -3x2

Reorder the terms:
42x + -2x2 = -29x + 29x + 3x2 + -3x2

Combine like terms: -29x + 29x = 0
42x + -2x2 = 0 + 3x2 + -3x2
42x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
42x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(21 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {0, 21}

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