[(s+2t)-(2s+3t)]-[(2s+3t)-(-4s+5t)]=0

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Solution for [(s+2t)-(2s+3t)]-[(2s+3t)-(-4s+5t)]=0 equation:


Simplifying
[(s + 2t) + -1(2s + 3t)] + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Remove parenthesis around (s + 2t)
[s + 2t + -1(2s + 3t)] + -1[(2s + 3t) + -1(-4s + 5t)] = 0
[s + 2t + (2s * -1 + 3t * -1)] + -1[(2s + 3t) + -1(-4s + 5t)] = 0
[s + 2t + (-2s + -3t)] + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Reorder the terms:
[s + -2s + 2t + -3t] + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Combine like terms: s + -2s = -1s
[-1s + 2t + -3t] + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Combine like terms: 2t + -3t = -1t
[-1s + -1t] + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Remove brackets around [-1s + -1t]
-1s + -1t + -1[(2s + 3t) + -1(-4s + 5t)] = 0

Remove parenthesis around (2s + 3t)
-1s + -1t + -1[2s + 3t + -1(-4s + 5t)] = 0
-1s + -1t + -1[2s + 3t + (-4s * -1 + 5t * -1)] = 0
-1s + -1t + -1[2s + 3t + (4s + -5t)] = 0

Reorder the terms:
-1s + -1t + -1[2s + 4s + 3t + -5t] = 0

Combine like terms: 2s + 4s = 6s
-1s + -1t + -1[6s + 3t + -5t] = 0

Combine like terms: 3t + -5t = -2t
-1s + -1t + -1[6s + -2t] = 0
-1s + -1t + [6s * -1 + -2t * -1] = 0
-1s + -1t + [-6s + 2t] = 0

Reorder the terms:
-1s + -6s + -1t + 2t = 0

Combine like terms: -1s + -6s = -7s
-7s + -1t + 2t = 0

Combine like terms: -1t + 2t = 1t
-7s + 1t = 0

Solving
-7s + 1t = 0

Solving for variable 's'.

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

Add '-1t' to each side of the equation.
-7s + 1t + -1t = 0 + -1t

Combine like terms: 1t + -1t = 0
-7s + 0 = 0 + -1t
-7s = 0 + -1t
Remove the zero:
-7s = -1t

Divide each side by '-7'.
s = 0.1428571429t

Simplifying
s = 0.1428571429t

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