5(t-1)+2(t-1)=2(t-2)+10(t+2)

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Solution for 5(t-1)+2(t-1)=2(t-2)+10(t+2) equation: 


Simplifying
5(t + -1) + 2(t + -1) = 2(t + -2) + 10(t + 2)

Reorder the terms:
5(-1 + t) + 2(t + -1) = 2(t + -2) + 10(t + 2)
(-1 * 5 + t * 5) + 2(t + -1) = 2(t + -2) + 10(t + 2)
(-5 + 5t) + 2(t + -1) = 2(t + -2) + 10(t + 2)

Reorder the terms:
-5 + 5t + 2(-1 + t) = 2(t + -2) + 10(t + 2)
-5 + 5t + (-1 * 2 + t * 2) = 2(t + -2) + 10(t + 2)
-5 + 5t + (-2 + 2t) = 2(t + -2) + 10(t + 2)

Reorder the terms:
-5 + -2 + 5t + 2t = 2(t + -2) + 10(t + 2)

Combine like terms: -5 + -2 = -7
-7 + 5t + 2t = 2(t + -2) + 10(t + 2)

Combine like terms: 5t + 2t = 7t
-7 + 7t = 2(t + -2) + 10(t + 2)

Reorder the terms:
-7 + 7t = 2(-2 + t) + 10(t + 2)
-7 + 7t = (-2 * 2 + t * 2) + 10(t + 2)
-7 + 7t = (-4 + 2t) + 10(t + 2)

Reorder the terms:
-7 + 7t = -4 + 2t + 10(2 + t)
-7 + 7t = -4 + 2t + (2 * 10 + t * 10)
-7 + 7t = -4 + 2t + (20 + 10t)

Reorder the terms:
-7 + 7t = -4 + 20 + 2t + 10t

Combine like terms: -4 + 20 = 16
-7 + 7t = 16 + 2t + 10t

Combine like terms: 2t + 10t = 12t
-7 + 7t = 16 + 12t

Solving
-7 + 7t = 16 + 12t

Solving for variable 't'.

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

Add '-12t' to each side of the equation.
-7 + 7t + -12t = 16 + 12t + -12t

Combine like terms: 7t + -12t = -5t
-7 + -5t = 16 + 12t + -12t

Combine like terms: 12t + -12t = 0
-7 + -5t = 16 + 0
-7 + -5t = 16

Add '7' to each side of the equation.
-7 + 7 + -5t = 16 + 7

Combine like terms: -7 + 7 = 0
0 + -5t = 16 + 7
-5t = 16 + 7

Combine like terms: 16 + 7 = 23
-5t = 23

Divide each side by '-5'.
t = -4.6

Simplifying
t = -4.6

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