n-1(4n-7)=5n-1(n+21)

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Solution for n-1(4n-7)=5n-1(n+21) equation:


Simplifying
n + -1(4n + -7) = 5n + -1(n + 21)

Reorder the terms:
n + -1(-7 + 4n) = 5n + -1(n + 21)
n + (-7 * -1 + 4n * -1) = 5n + -1(n + 21)
n + (7 + -4n) = 5n + -1(n + 21)

Reorder the terms:
7 + n + -4n = 5n + -1(n + 21)

Combine like terms: n + -4n = -3n
7 + -3n = 5n + -1(n + 21)

Reorder the terms:
7 + -3n = 5n + -1(21 + n)
7 + -3n = 5n + (21 * -1 + n * -1)
7 + -3n = 5n + (-21 + -1n)

Reorder the terms:
7 + -3n = -21 + 5n + -1n

Combine like terms: 5n + -1n = 4n
7 + -3n = -21 + 4n

Solving
7 + -3n = -21 + 4n

Solving for variable 'n'.

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

Add '-4n' to each side of the equation.
7 + -3n + -4n = -21 + 4n + -4n

Combine like terms: -3n + -4n = -7n
7 + -7n = -21 + 4n + -4n

Combine like terms: 4n + -4n = 0
7 + -7n = -21 + 0
7 + -7n = -21

Add '-7' to each side of the equation.
7 + -7 + -7n = -21 + -7

Combine like terms: 7 + -7 = 0
0 + -7n = -21 + -7
-7n = -21 + -7

Combine like terms: -21 + -7 = -28
-7n = -28

Divide each side by '-7'.
n = 4

Simplifying
n = 4

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