3[5-3(6-t)]-2=5[3(5t-4)+8]-56

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Solution for 3[5-3(6-t)]-2=5[3(5t-4)+8]-56 equation: 


Simplifying
3[5 + -3(6 + -1t)] + -2 = 5[3(5t + -4) + 8] + -56
3[5 + (6 * -3 + -1t * -3)] + -2 = 5[3(5t + -4) + 8] + -56
3[5 + (-18 + 3t)] + -2 = 5[3(5t + -4) + 8] + -56

Combine like terms: 5 + -18 = -13
3[-13 + 3t] + -2 = 5[3(5t + -4) + 8] + -56
[-13 * 3 + 3t * 3] + -2 = 5[3(5t + -4) + 8] + -56
[-39 + 9t] + -2 = 5[3(5t + -4) + 8] + -56

Reorder the terms:
-39 + -2 + 9t = 5[3(5t + -4) + 8] + -56

Combine like terms: -39 + -2 = -41
-41 + 9t = 5[3(5t + -4) + 8] + -56

Reorder the terms:
-41 + 9t = 5[3(-4 + 5t) + 8] + -56
-41 + 9t = 5[(-4 * 3 + 5t * 3) + 8] + -56
-41 + 9t = 5[(-12 + 15t) + 8] + -56

Reorder the terms:
-41 + 9t = 5[-12 + 8 + 15t] + -56

Combine like terms: -12 + 8 = -4
-41 + 9t = 5[-4 + 15t] + -56
-41 + 9t = [-4 * 5 + 15t * 5] + -56
-41 + 9t = [-20 + 75t] + -56

Reorder the terms:
-41 + 9t = -20 + -56 + 75t

Combine like terms: -20 + -56 = -76
-41 + 9t = -76 + 75t

Solving
-41 + 9t = -76 + 75t

Solving for variable 't'.

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

Add '-75t' to each side of the equation.
-41 + 9t + -75t = -76 + 75t + -75t

Combine like terms: 9t + -75t = -66t
-41 + -66t = -76 + 75t + -75t

Combine like terms: 75t + -75t = 0
-41 + -66t = -76 + 0
-41 + -66t = -76

Add '41' to each side of the equation.
-41 + 41 + -66t = -76 + 41

Combine like terms: -41 + 41 = 0
0 + -66t = -76 + 41
-66t = -76 + 41

Combine like terms: -76 + 41 = -35
-66t = -35

Divide each side by '-66'.
t = 0.5303030303

Simplifying
t = 0.5303030303

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