4-2r=3(5-r)+7z(r+1)

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Solution for 4-2r=3(5-r)+7z(r+1) equation: 


Simplifying
4 + -2r = 3(5 + -1r) + 7z(r + 1)
4 + -2r = (5 * 3 + -1r * 3) + 7z(r + 1)
4 + -2r = (15 + -3r) + 7z(r + 1)

Reorder the terms:
4 + -2r = 15 + -3r + 7z(1 + r)
4 + -2r = 15 + -3r + (1 * 7z + r * 7z)

Reorder the terms:
4 + -2r = 15 + -3r + (7rz + 7z)
4 + -2r = 15 + -3r + (7rz + 7z)

Solving
4 + -2r = 15 + -3r + 7rz + 7z

Solving for variable 'r'.

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

Add '3r' to each side of the equation.
4 + -2r + 3r = 15 + -3r + 7rz + 3r + 7z

Combine like terms: -2r + 3r = 1r
4 + 1r = 15 + -3r + 7rz + 3r + 7z

Reorder the terms:
4 + 1r = 15 + -3r + 3r + 7rz + 7z

Combine like terms: -3r + 3r = 0
4 + 1r = 15 + 0 + 7rz + 7z
4 + 1r = 15 + 7rz + 7z

Add '-7rz' to each side of the equation.
4 + 1r + -7rz = 15 + 7rz + -7rz + 7z

Combine like terms: 7rz + -7rz = 0
4 + 1r + -7rz = 15 + 0 + 7z
4 + 1r + -7rz = 15 + 7z

Add '-4' to each side of the equation.
4 + 1r + -4 + -7rz = 15 + -4 + 7z

Reorder the terms:
4 + -4 + 1r + -7rz = 15 + -4 + 7z

Combine like terms: 4 + -4 = 0
0 + 1r + -7rz = 15 + -4 + 7z
1r + -7rz = 15 + -4 + 7z

Combine like terms: 15 + -4 = 11
1r + -7rz = 11 + 7z

Reorder the terms:
-11 + 1r + -7rz + -7z = 11 + 7z + -11 + -7z

Reorder the terms:
-11 + 1r + -7rz + -7z = 11 + -11 + 7z + -7z

Combine like terms: 11 + -11 = 0
-11 + 1r + -7rz + -7z = 0 + 7z + -7z
-11 + 1r + -7rz + -7z = 7z + -7z

Combine like terms: 7z + -7z = 0
-11 + 1r + -7rz + -7z = 0

The solution to this equation could not be determined.

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