4t+g-r+(gh+rc)=v+w

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Solution for 4t+g-r+(gh+rc)=v+w equation: 


Simplifying
4t + g + -1r + (gh + rc) = v + w

Reorder the terms:
4t + g + -1r + (cr + gh) = v + w

Remove parenthesis around (cr + gh)
4t + g + -1r + cr + gh = v + w

Reorder the terms:
cr + g + gh + -1r + 4t = v + w

Solving
cr + g + gh + -1r + 4t = v + w

Solving for variable 'c'.

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

Add '-1g' to each side of the equation.
cr + g + gh + -1r + -1g + 4t = v + -1g + w

Reorder the terms:
cr + g + -1g + gh + -1r + 4t = v + -1g + w

Combine like terms: g + -1g = 0
cr + 0 + gh + -1r + 4t = v + -1g + w
cr + gh + -1r + 4t = v + -1g + w

Reorder the terms:
cr + gh + -1r + 4t = -1g + v + w

Add '-1gh' to each side of the equation.
cr + gh + -1r + -1gh + 4t = -1g + v + -1gh + w

Reorder the terms:
cr + gh + -1gh + -1r + 4t = -1g + v + -1gh + w

Combine like terms: gh + -1gh = 0
cr + 0 + -1r + 4t = -1g + v + -1gh + w
cr + -1r + 4t = -1g + v + -1gh + w

Reorder the terms:
cr + -1r + 4t = -1g + -1gh + v + w

Add 'r' to each side of the equation.
cr + -1r + r + 4t = -1g + -1gh + v + r + w

Combine like terms: -1r + r = 0
cr + 0 + 4t = -1g + -1gh + v + r + w
cr + 4t = -1g + -1gh + v + r + w

Reorder the terms:
cr + 4t = -1g + -1gh + r + v + w

Add '-4t' to each side of the equation.
cr + 4t + -4t = -1g + -1gh + r + v + -4t + w

Combine like terms: 4t + -4t = 0
cr + 0 = -1g + -1gh + r + v + -4t + w
cr = -1g + -1gh + r + v + -4t + w

Reorder the terms:
cr = -1g + -1gh + r + -4t + v + w

Divide each side by 'r'.
c = -1gr-1 + -1ghr-1 + 1 + -4r-1t + r-1v + r-1w

Simplifying
c = -1gr-1 + -1ghr-1 + 1 + -4r-1t + r-1v + r-1w

Reorder the terms:
c = 1 + -1ghr-1 + -1gr-1 + -4r-1t + r-1v + r-1w

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