y=50+.8*(t-[10+.25y])+100

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Solution for y=50+.8*(t-[10+.25y])+100 equation: 


Simplifying
y = 50 + 0.8(t + -1[10 + 0.25y]) + 100
y = 50 + 0.8(t + [10 * -1 + 0.25y * -1]) + 100
y = 50 + 0.8(t + [-10 + -0.25y]) + 100

Reorder the terms:
y = 50 + 0.8(-10 + t + -0.25y) + 100
y = 50 + (-10 * 0.8 + t * 0.8 + -0.25y * 0.8) + 100
y = 50 + (-8 + 0.8t + -0.2y) + 100

Reorder the terms:
y = 50 + -8 + 100 + 0.8t + -0.2y

Combine like terms: 50 + -8 = 42
y = 42 + 100 + 0.8t + -0.2y

Combine like terms: 42 + 100 = 142
y = 142 + 0.8t + -0.2y

Solving
y = 142 + 0.8t + -0.2y

Solving for variable 'y'.

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

Add '0.2y' to each side of the equation.
y + 0.2y = 142 + 0.8t + -0.2y + 0.2y

Combine like terms: y + 0.2y = 1.2y
1.2y = 142 + 0.8t + -0.2y + 0.2y

Combine like terms: -0.2y + 0.2y = 0.0
1.2y = 142 + 0.8t + 0.0
1.2y = 142 + 0.8t

Divide each side by '1.2'.
y = 118.3333333 + 0.6666666667t

Simplifying
y = 118.3333333 + 0.6666666667t

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