4[5-4(3-t)]-2=5[4(5t-4)+13]-38

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Solution for 4[5-4(3-t)]-2=5[4(5t-4)+13]-38 equation: 


Simplifying
4[5 + -4(3 + -1t)] + -2 = 5[4(5t + -4) + 13] + -38
4[5 + (3 * -4 + -1t * -4)] + -2 = 5[4(5t + -4) + 13] + -38
4[5 + (-12 + 4t)] + -2 = 5[4(5t + -4) + 13] + -38

Combine like terms: 5 + -12 = -7
4[-7 + 4t] + -2 = 5[4(5t + -4) + 13] + -38
[-7 * 4 + 4t * 4] + -2 = 5[4(5t + -4) + 13] + -38
[-28 + 16t] + -2 = 5[4(5t + -4) + 13] + -38

Reorder the terms:
-28 + -2 + 16t = 5[4(5t + -4) + 13] + -38

Combine like terms: -28 + -2 = -30
-30 + 16t = 5[4(5t + -4) + 13] + -38

Reorder the terms:
-30 + 16t = 5[4(-4 + 5t) + 13] + -38
-30 + 16t = 5[(-4 * 4 + 5t * 4) + 13] + -38
-30 + 16t = 5[(-16 + 20t) + 13] + -38

Reorder the terms:
-30 + 16t = 5[-16 + 13 + 20t] + -38

Combine like terms: -16 + 13 = -3
-30 + 16t = 5[-3 + 20t] + -38
-30 + 16t = [-3 * 5 + 20t * 5] + -38
-30 + 16t = [-15 + 100t] + -38

Reorder the terms:
-30 + 16t = -15 + -38 + 100t

Combine like terms: -15 + -38 = -53
-30 + 16t = -53 + 100t

Solving
-30 + 16t = -53 + 100t

Solving for variable 't'.

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

Add '-100t' to each side of the equation.
-30 + 16t + -100t = -53 + 100t + -100t

Combine like terms: 16t + -100t = -84t
-30 + -84t = -53 + 100t + -100t

Combine like terms: 100t + -100t = 0
-30 + -84t = -53 + 0
-30 + -84t = -53

Add '30' to each side of the equation.
-30 + 30 + -84t = -53 + 30

Combine like terms: -30 + 30 = 0
0 + -84t = -53 + 30
-84t = -53 + 30

Combine like terms: -53 + 30 = -23
-84t = -23

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

Simplifying
t = 0.2738095238

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