2[t-(3t-13)+10]=2(t-3)

Solution for 2[t-(3t-13)+10]=2(t-3) equation:

Simplifying
2[t + -1(3t + -13) + 10] = 2(t + -3)

Reorder the terms:
2[t + -1(-13 + 3t) + 10] = 2(t + -3)
2[t + (-13 * -1 + 3t * -1) + 10] = 2(t + -3)
2[t + (13 + -3t) + 10] = 2(t + -3)

Reorder the terms:
2[13 + 10 + t + -3t] = 2(t + -3)

Combine like terms: 13 + 10 = 23
2[23 + t + -3t] = 2(t + -3)

Combine like terms: t + -3t = -2t
2[23 + -2t] = 2(t + -3)
[23 * 2 + -2t * 2] = 2(t + -3)
[46 + -4t] = 2(t + -3)

Reorder the terms:
46 + -4t = 2(-3 + t)
46 + -4t = (-3 * 2 + t * 2)
46 + -4t = (-6 + 2t)

Solving
46 + -4t = -6 + 2t

Solving for variable 't'.

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

Add '-2t' to each side of the equation.
46 + -4t + -2t = -6 + 2t + -2t

Combine like terms: -4t + -2t = -6t
46 + -6t = -6 + 2t + -2t

Combine like terms: 2t + -2t = 0
46 + -6t = -6 + 0
46 + -6t = -6

Add '-46' to each side of the equation.
46 + -46 + -6t = -6 + -46

Combine like terms: 46 + -46 = 0
0 + -6t = -6 + -46
-6t = -6 + -46

Combine like terms: -6 + -46 = -52
-6t = -52

Divide each side by '-6'.
t = 8.666666667

Simplifying
t = 8.666666667