in(x+19)=in(7x-8)

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Solution for in(x+19)=in(7x-8) equation:


Simplifying
in(x + 19) = in(7x + -8)

Reorder the terms:
in(19 + x) = in(7x + -8)
(19 * in + x * in) = in(7x + -8)
(19in + inx) = in(7x + -8)

Reorder the terms:
19in + inx = in(-8 + 7x)
19in + inx = (-8 * in + 7x * in)
19in + inx = (-8in + 7inx)

Solving
19in + inx = -8in + 7inx

Solving for variable 'i'.

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

Add '8in' to each side of the equation.
19in + 8in + inx = -8in + 8in + 7inx

Combine like terms: 19in + 8in = 27in
27in + inx = -8in + 8in + 7inx

Combine like terms: -8in + 8in = 0
27in + inx = 0 + 7inx
27in + inx = 7inx

Add '-7inx' to each side of the equation.
27in + inx + -7inx = 7inx + -7inx

Combine like terms: inx + -7inx = -6inx
27in + -6inx = 7inx + -7inx

Combine like terms: 7inx + -7inx = 0
27in + -6inx = 0

Factor out the Greatest Common Factor (GCF), '3in'.
3in(9 + -2x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'in' equal to zero and attempt to solve: Simplifying in = 0 Solving in = 0 Move all terms containing i to the left, all other terms to the right. Simplifying in = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Add '2x' to each side of the equation. -2x + 2x = -9 + 2x Combine like terms: -2x + 2x = 0 0 = -9 + 2x Simplifying 0 = -9 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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