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 = 24
-7 + 7t = 24 + -2t + 10t

Combine like terms: -2t + 10t = 8t
-7 + 7t = 24 + 8t

Solving
-7 + 7t = 24 + 8t

Solving for variable 't'.

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

Add '-8t' to each side of the equation.
-7 + 7t + -8t = 24 + 8t + -8t

Combine like terms: 7t + -8t = -1t
-7 + -1t = 24 + 8t + -8t

Combine like terms: 8t + -8t = 0
-7 + -1t = 24 + 0
-7 + -1t = 24

Add '7' to each side of the equation.
-7 + 7 + -1t = 24 + 7

Combine like terms: -7 + 7 = 0
0 + -1t = 24 + 7
-1t = 24 + 7

Combine like terms: 24 + 7 = 31
-1t = 31

Divide each side by '-1'.
t = -31

Simplifying
t = -31

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