(X-45)(x-45)+x(x-45)+x=540

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Solution for (X-45)(x-45)+x(x-45)+x=540 equation: 


Simplifying
(X + -45)(x + -45) + x(x + -45) + x = 540

Reorder the terms:
(-45 + X)(x + -45) + x(x + -45) + x = 540

Reorder the terms:
(-45 + X)(-45 + x) + x(x + -45) + x = 540

Multiply (-45 + X) * (-45 + x)
(-45(-45 + x) + X(-45 + x)) + x(x + -45) + x = 540
((-45 * -45 + x * -45) + X(-45 + x)) + x(x + -45) + x = 540
((2025 + -45x) + X(-45 + x)) + x(x + -45) + x = 540
(2025 + -45x + (-45 * X + x * X)) + x(x + -45) + x = 540
(2025 + -45x + (-45X + xX)) + x(x + -45) + x = 540

Reorder the terms:
(2025 + -45X + -45x + xX) + x(x + -45) + x = 540
(2025 + -45X + -45x + xX) + x(x + -45) + x = 540

Reorder the terms:
2025 + -45X + -45x + xX + x(-45 + x) + x = 540
2025 + -45X + -45x + xX + (-45 * x + x * x) + x = 540
2025 + -45X + -45x + xX + (-45x + x2) + x = 540

Reorder the terms:
2025 + -45X + -45x + -45x + x + xX + x2 = 540

Combine like terms: -45x + -45x = -90x
2025 + -45X + -90x + x + xX + x2 = 540

Combine like terms: -90x + x = -89x
2025 + -45X + -89x + xX + x2 = 540

Solving
2025 + -45X + -89x + xX + x2 = 540

Solving for variable 'X'.

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

Add '-2025' to each side of the equation.
2025 + -45X + -89x + xX + -2025 + x2 = 540 + -2025

Reorder the terms:
2025 + -2025 + -45X + -89x + xX + x2 = 540 + -2025

Combine like terms: 2025 + -2025 = 0
0 + -45X + -89x + xX + x2 = 540 + -2025
-45X + -89x + xX + x2 = 540 + -2025

Combine like terms: 540 + -2025 = -1485
-45X + -89x + xX + x2 = -1485

Add '89x' to each side of the equation.
-45X + -89x + xX + 89x + x2 = -1485 + 89x

Reorder the terms:
-45X + -89x + 89x + xX + x2 = -1485 + 89x

Combine like terms: -89x + 89x = 0
-45X + 0 + xX + x2 = -1485 + 89x
-45X + xX + x2 = -1485 + 89x

Add '-1x2' to each side of the equation.
-45X + xX + x2 + -1x2 = -1485 + 89x + -1x2

Combine like terms: x2 + -1x2 = 0
-45X + xX + 0 = -1485 + 89x + -1x2
-45X + xX = -1485 + 89x + -1x2

Reorder the terms:
1485 + -45X + -89x + xX + x2 = -1485 + 89x + -1x2 + 1485 + -89x + x2

Reorder the terms:
1485 + -45X + -89x + xX + x2 = -1485 + 1485 + 89x + -89x + -1x2 + x2

Combine like terms: -1485 + 1485 = 0
1485 + -45X + -89x + xX + x2 = 0 + 89x + -89x + -1x2 + x2
1485 + -45X + -89x + xX + x2 = 89x + -89x + -1x2 + x2

Combine like terms: 89x + -89x = 0
1485 + -45X + -89x + xX + x2 = 0 + -1x2 + x2
1485 + -45X + -89x + xX + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1485 + -45X + -89x + xX + x2 = 0

The solution to this equation could not be determined.

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