6(T+2)+3(3-5T)=10(T-4)-6

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Solution for 6(T+2)+3(3-5T)=10(T-4)-6 equation: 


Simplifying
6(T + 2) + 3(3 + -5T) = 10(T + -4) + -6

Reorder the terms:
6(2 + T) + 3(3 + -5T) = 10(T + -4) + -6
(2 * 6 + T * 6) + 3(3 + -5T) = 10(T + -4) + -6
(12 + 6T) + 3(3 + -5T) = 10(T + -4) + -6
12 + 6T + (3 * 3 + -5T * 3) = 10(T + -4) + -6
12 + 6T + (9 + -15T) = 10(T + -4) + -6

Reorder the terms:
12 + 9 + 6T + -15T = 10(T + -4) + -6

Combine like terms: 12 + 9 = 21
21 + 6T + -15T = 10(T + -4) + -6

Combine like terms: 6T + -15T = -9T
21 + -9T = 10(T + -4) + -6

Reorder the terms:
21 + -9T = 10(-4 + T) + -6
21 + -9T = (-4 * 10 + T * 10) + -6
21 + -9T = (-40 + 10T) + -6

Reorder the terms:
21 + -9T = -40 + -6 + 10T

Combine like terms: -40 + -6 = -46
21 + -9T = -46 + 10T

Solving
21 + -9T = -46 + 10T

Solving for variable 'T'.

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

Add '-10T' to each side of the equation.
21 + -9T + -10T = -46 + 10T + -10T

Combine like terms: -9T + -10T = -19T
21 + -19T = -46 + 10T + -10T

Combine like terms: 10T + -10T = 0
21 + -19T = -46 + 0
21 + -19T = -46

Add '-21' to each side of the equation.
21 + -21 + -19T = -46 + -21

Combine like terms: 21 + -21 = 0
0 + -19T = -46 + -21
-19T = -46 + -21

Combine like terms: -46 + -21 = -67
-19T = -67

Divide each side by '-19'.
T = 3.526315789

Simplifying
T = 3.526315789

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