-((80)(967)(T-85)+(400)(4186)(T-85))=(45)(500)(T-22)

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Solution for -((80)(967)(T-85)+(400)(4186)(T-85))=(45)(500)(T-22) equation:


Simplifying
-1((80)(967)(T + -85) + (400)(4186)(T + -85)) = (45)(500)(T + -22)

Reorder the terms:
-1(80 * 967(-85 + T) + (400)(4186)(T + -85)) = (45)(500)(T + -22)

Multiply 80 * 967
-1(77360(-85 + T) + (400)(4186)(T + -85)) = (45)(500)(T + -22)
-1((-85 * 77360 + T * 77360) + (400)(4186)(T + -85)) = (45)(500)(T + -22)
-1((-6575600 + 77360T) + (400)(4186)(T + -85)) = (45)(500)(T + -22)

Reorder the terms:
-1(-6575600 + 77360T + 400 * 4186(-85 + T)) = (45)(500)(T + -22)

Multiply 400 * 4186
-1(-6575600 + 77360T + 1674400(-85 + T)) = (45)(500)(T + -22)
-1(-6575600 + 77360T + (-85 * 1674400 + T * 1674400)) = (45)(500)(T + -22)
-1(-6575600 + 77360T + (-142324000 + 1674400T)) = (45)(500)(T + -22)

Reorder the terms:
-1(-6575600 + -142324000 + 77360T + 1674400T) = (45)(500)(T + -22)

Combine like terms: -6575600 + -142324000 = -148899600
-1(-148899600 + 77360T + 1674400T) = (45)(500)(T + -22)

Combine like terms: 77360T + 1674400T = 1751760T
-1(-148899600 + 1751760T) = (45)(500)(T + -22)
(-148899600 * -1 + 1751760T * -1) = (45)(500)(T + -22)
(148899600 + -1751760T) = (45)(500)(T + -22)

Reorder the terms:
148899600 + -1751760T = 45 * 500(-22 + T)

Multiply 45 * 500
148899600 + -1751760T = 22500(-22 + T)
148899600 + -1751760T = (-22 * 22500 + T * 22500)
148899600 + -1751760T = (-495000 + 22500T)

Solving
148899600 + -1751760T = -495000 + 22500T

Solving for variable 'T'.

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

Add '-22500T' to each side of the equation.
148899600 + -1751760T + -22500T = -495000 + 22500T + -22500T

Combine like terms: -1751760T + -22500T = -1774260T
148899600 + -1774260T = -495000 + 22500T + -22500T

Combine like terms: 22500T + -22500T = 0
148899600 + -1774260T = -495000 + 0
148899600 + -1774260T = -495000

Add '-148899600' to each side of the equation.
148899600 + -148899600 + -1774260T = -495000 + -148899600

Combine like terms: 148899600 + -148899600 = 0
0 + -1774260T = -495000 + -148899600
-1774260T = -495000 + -148899600

Combine like terms: -495000 + -148899600 = -149394600
-1774260T = -149394600

Divide each side by '-1774260'.
T = 84.20107538

Simplifying
T = 84.20107538

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