6[4-2(6+3t)]=5[3(7-t)-4(8+2t)]-20

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Solution for 6[4-2(6+3t)]=5[3(7-t)-4(8+2t)]-20 equation: 


Simplifying
6[4 + -2(6 + 3t)] = 5[3(7 + -1t) + -4(8 + 2t)] + -20
6[4 + (6 * -2 + 3t * -2)] = 5[3(7 + -1t) + -4(8 + 2t)] + -20
6[4 + (-12 + -6t)] = 5[3(7 + -1t) + -4(8 + 2t)] + -20

Combine like terms: 4 + -12 = -8
6[-8 + -6t] = 5[3(7 + -1t) + -4(8 + 2t)] + -20
[-8 * 6 + -6t * 6] = 5[3(7 + -1t) + -4(8 + 2t)] + -20
[-48 + -36t] = 5[3(7 + -1t) + -4(8 + 2t)] + -20
-48 + -36t = 5[(7 * 3 + -1t * 3) + -4(8 + 2t)] + -20
-48 + -36t = 5[(21 + -3t) + -4(8 + 2t)] + -20
-48 + -36t = 5[21 + -3t + (8 * -4 + 2t * -4)] + -20
-48 + -36t = 5[21 + -3t + (-32 + -8t)] + -20

Reorder the terms:
-48 + -36t = 5[21 + -32 + -3t + -8t] + -20

Combine like terms: 21 + -32 = -11
-48 + -36t = 5[-11 + -3t + -8t] + -20

Combine like terms: -3t + -8t = -11t
-48 + -36t = 5[-11 + -11t] + -20
-48 + -36t = [-11 * 5 + -11t * 5] + -20
-48 + -36t = [-55 + -55t] + -20

Reorder the terms:
-48 + -36t = -55 + -20 + -55t

Combine like terms: -55 + -20 = -75
-48 + -36t = -75 + -55t

Solving
-48 + -36t = -75 + -55t

Solving for variable 't'.

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

Add '55t' to each side of the equation.
-48 + -36t + 55t = -75 + -55t + 55t

Combine like terms: -36t + 55t = 19t
-48 + 19t = -75 + -55t + 55t

Combine like terms: -55t + 55t = 0
-48 + 19t = -75 + 0
-48 + 19t = -75

Add '48' to each side of the equation.
-48 + 48 + 19t = -75 + 48

Combine like terms: -48 + 48 = 0
0 + 19t = -75 + 48
19t = -75 + 48

Combine like terms: -75 + 48 = -27
19t = -27

Divide each side by '19'.
t = -1.421052632

Simplifying
t = -1.421052632

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