(X-30)(x-30)+x(x-30)+x=540

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Solution for (X-30)(x-30)+x(x-30)+x=540 equation:


Simplifying
(X + -30)(x + -30) + x(x + -30) + x = 540

Reorder the terms:
(-30 + X)(x + -30) + x(x + -30) + x = 540

Reorder the terms:
(-30 + X)(-30 + x) + x(x + -30) + x = 540

Multiply (-30 + X) * (-30 + x)
(-30(-30 + x) + X(-30 + x)) + x(x + -30) + x = 540
((-30 * -30 + x * -30) + X(-30 + x)) + x(x + -30) + x = 540
((900 + -30x) + X(-30 + x)) + x(x + -30) + x = 540
(900 + -30x + (-30 * X + x * X)) + x(x + -30) + x = 540
(900 + -30x + (-30X + xX)) + x(x + -30) + x = 540

Reorder the terms:
(900 + -30X + -30x + xX) + x(x + -30) + x = 540
(900 + -30X + -30x + xX) + x(x + -30) + x = 540

Reorder the terms:
900 + -30X + -30x + xX + x(-30 + x) + x = 540
900 + -30X + -30x + xX + (-30 * x + x * x) + x = 540
900 + -30X + -30x + xX + (-30x + x2) + x = 540

Reorder the terms:
900 + -30X + -30x + -30x + x + xX + x2 = 540

Combine like terms: -30x + -30x = -60x
900 + -30X + -60x + x + xX + x2 = 540

Combine like terms: -60x + x = -59x
900 + -30X + -59x + xX + x2 = 540

Solving
900 + -30X + -59x + xX + x2 = 540

Solving for variable 'X'.

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

Add '-900' to each side of the equation.
900 + -30X + -59x + xX + -900 + x2 = 540 + -900

Reorder the terms:
900 + -900 + -30X + -59x + xX + x2 = 540 + -900

Combine like terms: 900 + -900 = 0
0 + -30X + -59x + xX + x2 = 540 + -900
-30X + -59x + xX + x2 = 540 + -900

Combine like terms: 540 + -900 = -360
-30X + -59x + xX + x2 = -360

Add '59x' to each side of the equation.
-30X + -59x + xX + 59x + x2 = -360 + 59x

Reorder the terms:
-30X + -59x + 59x + xX + x2 = -360 + 59x

Combine like terms: -59x + 59x = 0
-30X + 0 + xX + x2 = -360 + 59x
-30X + xX + x2 = -360 + 59x

Add '-1x2' to each side of the equation.
-30X + xX + x2 + -1x2 = -360 + 59x + -1x2

Combine like terms: x2 + -1x2 = 0
-30X + xX + 0 = -360 + 59x + -1x2
-30X + xX = -360 + 59x + -1x2

Reorder the terms:
360 + -30X + -59x + xX + x2 = -360 + 59x + -1x2 + 360 + -59x + x2

Reorder the terms:
360 + -30X + -59x + xX + x2 = -360 + 360 + 59x + -59x + -1x2 + x2

Combine like terms: -360 + 360 = 0
360 + -30X + -59x + xX + x2 = 0 + 59x + -59x + -1x2 + x2
360 + -30X + -59x + xX + x2 = 59x + -59x + -1x2 + x2

Combine like terms: 59x + -59x = 0
360 + -30X + -59x + xX + x2 = 0 + -1x2 + x2
360 + -30X + -59x + xX + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
360 + -30X + -59x + xX + x2 = 0

The solution to this equation could not be determined.

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