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

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

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

Reorder the terms:
2(-3 + t) + -3(3t + -4) = 10 + -6(5t + 2)
(-3 * 2 + t * 2) + -3(3t + -4) = 10 + -6(5t + 2)
(-6 + 2t) + -3(3t + -4) = 10 + -6(5t + 2)

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

Reorder the terms:
-6 + 12 + 2t + -9t = 10 + -6(5t + 2)

Combine like terms: -6 + 12 = 6
6 + 2t + -9t = 10 + -6(5t + 2)

Combine like terms: 2t + -9t = -7t
6 + -7t = 10 + -6(5t + 2)

Reorder the terms:
6 + -7t = 10 + -6(2 + 5t)
6 + -7t = 10 + (2 * -6 + 5t * -6)
6 + -7t = 10 + (-12 + -30t)

Combine like terms: 10 + -12 = -2
6 + -7t = -2 + -30t

Solving
6 + -7t = -2 + -30t

Solving for variable 't'.

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

Add '30t' to each side of the equation.
6 + -7t + 30t = -2 + -30t + 30t

Combine like terms: -7t + 30t = 23t
6 + 23t = -2 + -30t + 30t

Combine like terms: -30t + 30t = 0
6 + 23t = -2 + 0
6 + 23t = -2

Add '-6' to each side of the equation.
6 + -6 + 23t = -2 + -6

Combine like terms: 6 + -6 = 0
0 + 23t = -2 + -6
23t = -2 + -6

Combine like terms: -2 + -6 = -8
23t = -8

Divide each side by '23'.
t = -0.347826087

Simplifying
t = -0.347826087