(X+9)(5-x)=(9-x)(x+4)

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Solution for (X+9)(5-x)=(9-x)(x+4) equation: 


Simplifying
(X + 9)(5 + -1x) = (9 + -1x)(x + 4)

Reorder the terms:
(9 + X)(5 + -1x) = (9 + -1x)(x + 4)

Multiply (9 + X) * (5 + -1x)
(9(5 + -1x) + X(5 + -1x)) = (9 + -1x)(x + 4)
((5 * 9 + -1x * 9) + X(5 + -1x)) = (9 + -1x)(x + 4)
((45 + -9x) + X(5 + -1x)) = (9 + -1x)(x + 4)
(45 + -9x + (5 * X + -1x * X)) = (9 + -1x)(x + 4)
(45 + -9x + (5X + -1xX)) = (9 + -1x)(x + 4)

Reorder the terms:
(45 + 5X + -9x + -1xX) = (9 + -1x)(x + 4)
(45 + 5X + -9x + -1xX) = (9 + -1x)(x + 4)

Reorder the terms:
45 + 5X + -9x + -1xX = (9 + -1x)(4 + x)

Multiply (9 + -1x) * (4 + x)
45 + 5X + -9x + -1xX = (9(4 + x) + -1x * (4 + x))
45 + 5X + -9x + -1xX = ((4 * 9 + x * 9) + -1x * (4 + x))
45 + 5X + -9x + -1xX = ((36 + 9x) + -1x * (4 + x))
45 + 5X + -9x + -1xX = (36 + 9x + (4 * -1x + x * -1x))
45 + 5X + -9x + -1xX = (36 + 9x + (-4x + -1x2))

Combine like terms: 9x + -4x = 5x
45 + 5X + -9x + -1xX = (36 + 5x + -1x2)

Solving
45 + 5X + -9x + -1xX = 36 + 5x + -1x2

Solving for variable 'X'.

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

Add '-45' to each side of the equation.
45 + 5X + -9x + -45 + -1xX = 36 + 5x + -45 + -1x2

Reorder the terms:
45 + -45 + 5X + -9x + -1xX = 36 + 5x + -45 + -1x2

Combine like terms: 45 + -45 = 0
0 + 5X + -9x + -1xX = 36 + 5x + -45 + -1x2
5X + -9x + -1xX = 36 + 5x + -45 + -1x2

Reorder the terms:
5X + -9x + -1xX = 36 + -45 + 5x + -1x2

Combine like terms: 36 + -45 = -9
5X + -9x + -1xX = -9 + 5x + -1x2

Add '9x' to each side of the equation.
5X + -9x + 9x + -1xX = -9 + 5x + 9x + -1x2

Combine like terms: -9x + 9x = 0
5X + 0 + -1xX = -9 + 5x + 9x + -1x2
5X + -1xX = -9 + 5x + 9x + -1x2

Combine like terms: 5x + 9x = 14x
5X + -1xX = -9 + 14x + -1x2

Reorder the terms:
9 + 5X + -14x + -1xX + x2 = -9 + 14x + -1x2 + 9 + -14x + x2

Reorder the terms:
9 + 5X + -14x + -1xX + x2 = -9 + 9 + 14x + -14x + -1x2 + x2

Combine like terms: -9 + 9 = 0
9 + 5X + -14x + -1xX + x2 = 0 + 14x + -14x + -1x2 + x2
9 + 5X + -14x + -1xX + x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
9 + 5X + -14x + -1xX + x2 = 0 + -1x2 + x2
9 + 5X + -14x + -1xX + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
9 + 5X + -14x + -1xX + x2 = 0

The solution to this equation could not be determined.

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