3[5-3(6+t)]-3=5[3(5t-4)+8]-45

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Solution for 3[5-3(6+t)]-3=5[3(5t-4)+8]-45 equation: 


Simplifying
3[5 + -3(6 + t)] + -3 = 5[3(5t + -4) + 8] + -45
3[5 + (6 * -3 + t * -3)] + -3 = 5[3(5t + -4) + 8] + -45
3[5 + (-18 + -3t)] + -3 = 5[3(5t + -4) + 8] + -45

Combine like terms: 5 + -18 = -13
3[-13 + -3t] + -3 = 5[3(5t + -4) + 8] + -45
[-13 * 3 + -3t * 3] + -3 = 5[3(5t + -4) + 8] + -45
[-39 + -9t] + -3 = 5[3(5t + -4) + 8] + -45

Reorder the terms:
-39 + -3 + -9t = 5[3(5t + -4) + 8] + -45

Combine like terms: -39 + -3 = -42
-42 + -9t = 5[3(5t + -4) + 8] + -45

Reorder the terms:
-42 + -9t = 5[3(-4 + 5t) + 8] + -45
-42 + -9t = 5[(-4 * 3 + 5t * 3) + 8] + -45
-42 + -9t = 5[(-12 + 15t) + 8] + -45

Reorder the terms:
-42 + -9t = 5[-12 + 8 + 15t] + -45

Combine like terms: -12 + 8 = -4
-42 + -9t = 5[-4 + 15t] + -45
-42 + -9t = [-4 * 5 + 15t * 5] + -45
-42 + -9t = [-20 + 75t] + -45

Reorder the terms:
-42 + -9t = -20 + -45 + 75t

Combine like terms: -20 + -45 = -65
-42 + -9t = -65 + 75t

Solving
-42 + -9t = -65 + 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.
-42 + -9t + -75t = -65 + 75t + -75t

Combine like terms: -9t + -75t = -84t
-42 + -84t = -65 + 75t + -75t

Combine like terms: 75t + -75t = 0
-42 + -84t = -65 + 0
-42 + -84t = -65

Add '42' to each side of the equation.
-42 + 42 + -84t = -65 + 42

Combine like terms: -42 + 42 = 0
0 + -84t = -65 + 42
-84t = -65 + 42

Combine like terms: -65 + 42 = -23
-84t = -23

Divide each side by '-84'.
t = 0.2738095238

Simplifying
t = 0.2738095238

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