2r+4r(r+P+q)=u

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Solution for 2r+4r(r+P+q)=u equation: 


Simplifying
2r + 4r(r + P + q) = u

Reorder the terms:
2r + 4r(P + q + r) = u
2r + (P * 4r + q * 4r + r * 4r) = u

Reorder the terms:
2r + (4qr + 4rP + 4r2) = u
2r + (4qr + 4rP + 4r2) = u

Reorder the terms:
4qr + 2r + 4rP + 4r2 = u

Solving
4qr + 2r + 4rP + 4r2 = u

Solving for variable 'q'.

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

Add '-2r' to each side of the equation.
4qr + 2r + 4rP + -2r + 4r2 = -2r + u

Reorder the terms:
4qr + 2r + -2r + 4rP + 4r2 = -2r + u

Combine like terms: 2r + -2r = 0
4qr + 0 + 4rP + 4r2 = -2r + u
4qr + 4rP + 4r2 = -2r + u

Add '-4rP' to each side of the equation.
4qr + 4rP + -4rP + 4r2 = -2r + -4rP + u

Combine like terms: 4rP + -4rP = 0
4qr + 0 + 4r2 = -2r + -4rP + u
4qr + 4r2 = -2r + -4rP + u

Add '-4r2' to each side of the equation.
4qr + 4r2 + -4r2 = -2r + -4rP + -4r2 + u

Combine like terms: 4r2 + -4r2 = 0
4qr + 0 = -2r + -4rP + -4r2 + u
4qr = -2r + -4rP + -4r2 + u

Divide each side by '4r'.
q = -0.5 + -1P + -1r + 0.25r-1u

Simplifying
q = -0.5 + -1P + -1r + 0.25r-1u

Reorder the terms:
q = -0.5 + -1P + 0.25r-1u + -1r

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