3(px+qy)+5(rx+5y)=75x+100y

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Solution for 3(px+qy)+5(rx+5y)=75x+100y equation: 


Simplifying
3(px + qy) + 5(rx + 5y) = 75x + 100y
(px * 3 + qy * 3) + 5(rx + 5y) = 75x + 100y
(3px + 3qy) + 5(rx + 5y) = 75x + 100y
3px + 3qy + (rx * 5 + 5y * 5) = 75x + 100y
3px + 3qy + (5rx + 25y) = 75x + 100y

Solving
3px + 3qy + 5rx + 25y = 75x + 100y

Solving for variable 'p'.

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

Add '-3qy' to each side of the equation.
3px + 3qy + 5rx + -3qy + 25y = 75x + -3qy + 100y

Reorder the terms:
3px + 3qy + -3qy + 5rx + 25y = 75x + -3qy + 100y

Combine like terms: 3qy + -3qy = 0
3px + 0 + 5rx + 25y = 75x + -3qy + 100y
3px + 5rx + 25y = 75x + -3qy + 100y

Reorder the terms:
3px + 5rx + 25y = -3qy + 75x + 100y

Add '-5rx' to each side of the equation.
3px + 5rx + -5rx + 25y = -3qy + 75x + -5rx + 100y

Combine like terms: 5rx + -5rx = 0
3px + 0 + 25y = -3qy + 75x + -5rx + 100y
3px + 25y = -3qy + 75x + -5rx + 100y

Reorder the terms:
3px + 25y = -3qy + -5rx + 75x + 100y

Add '-25y' to each side of the equation.
3px + 25y + -25y = -3qy + -5rx + 75x + 100y + -25y

Combine like terms: 25y + -25y = 0
3px + 0 = -3qy + -5rx + 75x + 100y + -25y
3px = -3qy + -5rx + 75x + 100y + -25y

Combine like terms: 100y + -25y = 75y
3px = -3qy + -5rx + 75x + 75y

Divide each side by '3x'.
p = -1qx-1y + -1.666666667r + 25 + 25x-1y

Simplifying
p = -1qx-1y + -1.666666667r + 25 + 25x-1y

Reorder the terms:
p = 25 + -1qx-1y + -1.666666667r + 25x-1y

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