Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "g7"   was replaced by   "g^7". 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (22•23g78) +  91g  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   92g⁷⁸ + 91g  =   g • (92g⁷⁷ + 91) 

Equation at the end of step  3  :

  g • (92g77 + 91)  = 0 

Step  4  :

Theory - Roots of a product :

 4.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 4.2      Solve  :    g = 0 

  Solution is  g = 0

Solving a Single Variable Equation :

 4.3      Solve  :    92g⁷⁷+91 = 0 

 Subtract  91  from both sides of the equation : 
                      92g⁷⁷ = -91
Divide both sides of the equation by 92:
                     g⁷⁷ = -91/92 = -0.989
                     g  =  77th root of (-91/92) 

 Negative numbers have real 77th roots.
 77th root of (-91/92) = ⁷⁷√ -1• 91/92  = ⁷⁷√ -1 • ⁷⁷√ 91/92  =(-1)•⁷⁷√ 91/92 

The equation has one real solution, a negative number This solution is  g = 77th root of (-0.989) = -0.99986

Two solutions were found :

1.  g = 77th root of (-0.989) = -0.99986
2.  g = 0