(100)(0.22)(180-X)=(200)(X-10)+152(X-10)

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Solution for (100)(0.22)(180-X)=(200)(X-10)+152(X-10) equation: 


Simplifying
(100)(0.22)(180 + -1X) = (200)(X + -10) + 152(X + -10)

Multiply 100 * 0.22
22(180 + -1X) = (200)(X + -10) + 152(X + -10)
(180 * 22 + -1X * 22) = (200)(X + -10) + 152(X + -10)
(3960 + -22X) = (200)(X + -10) + 152(X + -10)

Reorder the terms:
3960 + -22X = 200(-10 + X) + 152(X + -10)
3960 + -22X = (-10 * 200 + X * 200) + 152(X + -10)
3960 + -22X = (-2000 + 200X) + 152(X + -10)

Reorder the terms:
3960 + -22X = -2000 + 200X + 152(-10 + X)
3960 + -22X = -2000 + 200X + (-10 * 152 + X * 152)
3960 + -22X = -2000 + 200X + (-1520 + 152X)

Reorder the terms:
3960 + -22X = -2000 + -1520 + 200X + 152X

Combine like terms: -2000 + -1520 = -3520
3960 + -22X = -3520 + 200X + 152X

Combine like terms: 200X + 152X = 352X
3960 + -22X = -3520 + 352X

Solving
3960 + -22X = -3520 + 352X

Solving for variable 'X'.

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

Add '-352X' to each side of the equation.
3960 + -22X + -352X = -3520 + 352X + -352X

Combine like terms: -22X + -352X = -374X
3960 + -374X = -3520 + 352X + -352X

Combine like terms: 352X + -352X = 0
3960 + -374X = -3520 + 0
3960 + -374X = -3520

Add '-3960' to each side of the equation.
3960 + -3960 + -374X = -3520 + -3960

Combine like terms: 3960 + -3960 = 0
0 + -374X = -3520 + -3960
-374X = -3520 + -3960

Combine like terms: -3520 + -3960 = -7480
-374X = -7480

Divide each side by '-374'.
X = 20

Simplifying
X = 20

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