(X-2)(x-5)=(x+5)(x+8)

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


Simplifying
(X + -2)(x + -5) = (x + 5)(x + 8)

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

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

Multiply (-2 + X) * (-5 + x)
(-2(-5 + x) + X(-5 + x)) = (x + 5)(x + 8)
((-5 * -2 + x * -2) + X(-5 + x)) = (x + 5)(x + 8)
((10 + -2x) + X(-5 + x)) = (x + 5)(x + 8)
(10 + -2x + (-5 * X + x * X)) = (x + 5)(x + 8)
(10 + -2x + (-5X + xX)) = (x + 5)(x + 8)

Reorder the terms:
(10 + -5X + -2x + xX) = (x + 5)(x + 8)
(10 + -5X + -2x + xX) = (x + 5)(x + 8)

Reorder the terms:
10 + -5X + -2x + xX = (5 + x)(x + 8)

Reorder the terms:
10 + -5X + -2x + xX = (5 + x)(8 + x)

Multiply (5 + x) * (8 + x)
10 + -5X + -2x + xX = (5(8 + x) + x(8 + x))
10 + -5X + -2x + xX = ((8 * 5 + x * 5) + x(8 + x))
10 + -5X + -2x + xX = ((40 + 5x) + x(8 + x))
10 + -5X + -2x + xX = (40 + 5x + (8 * x + x * x))
10 + -5X + -2x + xX = (40 + 5x + (8x + x2))

Combine like terms: 5x + 8x = 13x
10 + -5X + -2x + xX = (40 + 13x + x2)

Solving
10 + -5X + -2x + xX = 40 + 13x + x2

Solving for variable 'X'.

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

Add '-10' to each side of the equation.
10 + -5X + -2x + -10 + xX = 40 + 13x + -10 + x2

Reorder the terms:
10 + -10 + -5X + -2x + xX = 40 + 13x + -10 + x2

Combine like terms: 10 + -10 = 0
0 + -5X + -2x + xX = 40 + 13x + -10 + x2
-5X + -2x + xX = 40 + 13x + -10 + x2

Reorder the terms:
-5X + -2x + xX = 40 + -10 + 13x + x2

Combine like terms: 40 + -10 = 30
-5X + -2x + xX = 30 + 13x + x2

Add '2x' to each side of the equation.
-5X + -2x + 2x + xX = 30 + 13x + 2x + x2

Combine like terms: -2x + 2x = 0
-5X + 0 + xX = 30 + 13x + 2x + x2
-5X + xX = 30 + 13x + 2x + x2

Combine like terms: 13x + 2x = 15x
-5X + xX = 30 + 15x + x2

Reorder the terms:
-30 + -5X + -15x + xX + -1x2 = 30 + 15x + x2 + -30 + -15x + -1x2

Reorder the terms:
-30 + -5X + -15x + xX + -1x2 = 30 + -30 + 15x + -15x + x2 + -1x2

Combine like terms: 30 + -30 = 0
-30 + -5X + -15x + xX + -1x2 = 0 + 15x + -15x + x2 + -1x2
-30 + -5X + -15x + xX + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-30 + -5X + -15x + xX + -1x2 = 0 + x2 + -1x2
-30 + -5X + -15x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + -5X + -15x + xX + -1x2 = 0

The solution to this equation could not be determined.

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