(x^2-x-42)*lg(x+5)=0

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Solution for (x^2-x-42)*lg(x+5)=0 equation: 


Simplifying
(x2 + -1x + -42) * lg(x + 5) = 0

Reorder the terms:
(-42 + -1x + x2) * lg(x + 5) = 0

Reorder the terms:
(-42 + -1x + x2) * gl(5 + x) = 0

Reorder the terms for easier multiplication:
gl(-42 + -1x + x2)(5 + x) = 0

Multiply (-42 + -1x + x2) * (5 + x)
gl(-42(5 + x) + -1x * (5 + x) + x2(5 + x)) = 0
gl((5 * -42 + x * -42) + -1x * (5 + x) + x2(5 + x)) = 0
gl((-210 + -42x) + -1x * (5 + x) + x2(5 + x)) = 0
gl(-210 + -42x + (5 * -1x + x * -1x) + x2(5 + x)) = 0
gl(-210 + -42x + (-5x + -1x2) + x2(5 + x)) = 0
gl(-210 + -42x + -5x + -1x2 + (5 * x2 + x * x2)) = 0
gl(-210 + -42x + -5x + -1x2 + (5x2 + x3)) = 0

Combine like terms: -42x + -5x = -47x
gl(-210 + -47x + -1x2 + 5x2 + x3) = 0

Combine like terms: -1x2 + 5x2 = 4x2
gl(-210 + -47x + 4x2 + x3) = 0
(-210 * gl + -47x * gl + 4x2 * gl + x3 * gl) = 0
(-210gl + -47glx + 4glx2 + glx3) = 0

Solving
-210gl + -47glx + 4glx2 + glx3 = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-210 + -47x + 4x2 + x3) = 0


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

Simplifying
gl = 0

Solving
gl = 0

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

Simplifying
gl = 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 '(-210 + -47x + 4x2 + x3)' equal to zero and attempt to solve:

Simplifying
-210 + -47x + 4x2 + x3 = 0

Solving
-210 + -47x + 4x2 + x3 = 0

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

Add '210' to each side of the equation.
-210 + -47x + 4x2 + 210 + x3 = 0 + 210

Reorder the terms:
-210 + 210 + -47x + 4x2 + x3 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + -47x + 4x2 + x3 = 0 + 210
-47x + 4x2 + x3 = 0 + 210

Combine like terms: 0 + 210 = 210
-47x + 4x2 + x3 = 210

Add '47x' to each side of the equation.
-47x + 4x2 + 47x + x3 = 210 + 47x

Reorder the terms:
-47x + 47x + 4x2 + x3 = 210 + 47x

Combine like terms: -47x + 47x = 0
0 + 4x2 + x3 = 210 + 47x
4x2 + x3 = 210 + 47x

Add '-4x2' to each side of the equation.
4x2 + -4x2 + x3 = 210 + 47x + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + x3 = 210 + 47x + -4x2
x3 = 210 + 47x + -4x2

Add '-1x3' to each side of the equation.
x3 + -1x3 = 210 + 47x + -4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = 210 + 47x + -4x2 + -1x3

Simplifying
0 = 210 + 47x + -4x2 + -1x3

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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