2(t+9)+2(-3t-1)=-5(t-1)+1

Solution for 2(t+9)+2(-3t-1)=-5(t-1)+1 equation:

Simplifying
2(t + 9) + 2(-3t + -1) = -5(t + -1) + 1

Reorder the terms:
2(9 + t) + 2(-3t + -1) = -5(t + -1) + 1
(9 * 2 + t * 2) + 2(-3t + -1) = -5(t + -1) + 1
(18 + 2t) + 2(-3t + -1) = -5(t + -1) + 1

Reorder the terms:
18 + 2t + 2(-1 + -3t) = -5(t + -1) + 1
18 + 2t + (-1 * 2 + -3t * 2) = -5(t + -1) + 1
18 + 2t + (-2 + -6t) = -5(t + -1) + 1

Reorder the terms:
18 + -2 + 2t + -6t = -5(t + -1) + 1

Combine like terms: 18 + -2 = 16
16 + 2t + -6t = -5(t + -1) + 1

Combine like terms: 2t + -6t = -4t
16 + -4t = -5(t + -1) + 1

Reorder the terms:
16 + -4t = -5(-1 + t) + 1
16 + -4t = (-1 * -5 + t * -5) + 1
16 + -4t = (5 + -5t) + 1

Reorder the terms:
16 + -4t = 5 + 1 + -5t

Combine like terms: 5 + 1 = 6
16 + -4t = 6 + -5t

Solving
16 + -4t = 6 + -5t

Solving for variable 't'.

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

Add '5t' to each side of the equation.
16 + -4t + 5t = 6 + -5t + 5t

Combine like terms: -4t + 5t = 1t
16 + 1t = 6 + -5t + 5t

Combine like terms: -5t + 5t = 0
16 + 1t = 6 + 0
16 + 1t = 6

Add '-16' to each side of the equation.
16 + -16 + 1t = 6 + -16

Combine like terms: 16 + -16 = 0
0 + 1t = 6 + -16
1t = 6 + -16

Combine like terms: 6 + -16 = -10
1t = -10

Divide each side by '1'.
t = -10

Simplifying
t = -10