(54+9X)(6+x)=(12+8x)(15+x)

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Solution for (54+9X)(6+x)=(12+8x)(15+x) equation:


Simplifying
(54 + 9X)(6 + x) = (12 + 8x)(15 + x)

Multiply (54 + 9X) * (6 + x)
(54(6 + x) + 9X * (6 + x)) = (12 + 8x)(15 + x)
((6 * 54 + x * 54) + 9X * (6 + x)) = (12 + 8x)(15 + x)
((324 + 54x) + 9X * (6 + x)) = (12 + 8x)(15 + x)
(324 + 54x + (6 * 9X + x * 9X)) = (12 + 8x)(15 + x)
(324 + 54x + (54X + 9xX)) = (12 + 8x)(15 + x)

Reorder the terms:
(324 + 54X + 54x + 9xX) = (12 + 8x)(15 + x)
(324 + 54X + 54x + 9xX) = (12 + 8x)(15 + x)

Multiply (12 + 8x) * (15 + x)
324 + 54X + 54x + 9xX = (12(15 + x) + 8x * (15 + x))
324 + 54X + 54x + 9xX = ((15 * 12 + x * 12) + 8x * (15 + x))
324 + 54X + 54x + 9xX = ((180 + 12x) + 8x * (15 + x))
324 + 54X + 54x + 9xX = (180 + 12x + (15 * 8x + x * 8x))
324 + 54X + 54x + 9xX = (180 + 12x + (120x + 8x2))

Combine like terms: 12x + 120x = 132x
324 + 54X + 54x + 9xX = (180 + 132x + 8x2)

Solving
324 + 54X + 54x + 9xX = 180 + 132x + 8x2

Solving for variable 'X'.

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

Add '-324' to each side of the equation.
324 + 54X + 54x + -324 + 9xX = 180 + 132x + -324 + 8x2

Reorder the terms:
324 + -324 + 54X + 54x + 9xX = 180 + 132x + -324 + 8x2

Combine like terms: 324 + -324 = 0
0 + 54X + 54x + 9xX = 180 + 132x + -324 + 8x2
54X + 54x + 9xX = 180 + 132x + -324 + 8x2

Reorder the terms:
54X + 54x + 9xX = 180 + -324 + 132x + 8x2

Combine like terms: 180 + -324 = -144
54X + 54x + 9xX = -144 + 132x + 8x2

Add '-54x' to each side of the equation.
54X + 54x + -54x + 9xX = -144 + 132x + -54x + 8x2

Combine like terms: 54x + -54x = 0
54X + 0 + 9xX = -144 + 132x + -54x + 8x2
54X + 9xX = -144 + 132x + -54x + 8x2

Combine like terms: 132x + -54x = 78x
54X + 9xX = -144 + 78x + 8x2

Reorder the terms:
144 + 54X + -78x + 9xX + -8x2 = -144 + 78x + 8x2 + 144 + -78x + -8x2

Reorder the terms:
144 + 54X + -78x + 9xX + -8x2 = -144 + 144 + 78x + -78x + 8x2 + -8x2

Combine like terms: -144 + 144 = 0
144 + 54X + -78x + 9xX + -8x2 = 0 + 78x + -78x + 8x2 + -8x2
144 + 54X + -78x + 9xX + -8x2 = 78x + -78x + 8x2 + -8x2

Combine like terms: 78x + -78x = 0
144 + 54X + -78x + 9xX + -8x2 = 0 + 8x2 + -8x2
144 + 54X + -78x + 9xX + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
144 + 54X + -78x + 9xX + -8x2 = 0

The solution to this equation could not be determined.

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