tan(x+45)=8tan(x)

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Solution for tan(x+45)=8tan(x) equation: 


Simplifying
tan(x + 45) = 8tan(x)

Reorder the terms:
ant(45 + x) = 8tan(x)
(45 * ant + x * ant) = 8tan(x)
(45ant + antx) = 8tan(x)

Multiply ant * x
45ant + antx = 8antx

Solving
45ant + antx = 8antx

Solving for variable 'a'.

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

Add '-8antx' to each side of the equation.
45ant + antx + -8antx = 8antx + -8antx

Combine like terms: antx + -8antx = -7antx
45ant + -7antx = 8antx + -8antx

Combine like terms: 8antx + -8antx = 0
45ant + -7antx = 0

Factor out the Greatest Common Factor (GCF), 'ant'.
ant(45 + -7x) = 0


Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve:

Simplifying
ant = 0

Solving
ant = 0

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

Simplifying
ant = 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 '(45 + -7x)' equal to zero and attempt to solve:

Simplifying
45 + -7x = 0

Solving
45 + -7x = 0

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

Add '-45' to each side of the equation.
45 + -45 + -7x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -7x = 0 + -45
-7x = 0 + -45

Combine like terms: 0 + -45 = -45
-7x = -45

Add '7x' to each side of the equation.
-7x + 7x = -45 + 7x

Combine like terms: -7x + 7x = 0
0 = -45 + 7x

Simplifying
0 = -45 + 7x

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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