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Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

p*(x)-(-3*x^5+4*x^3-5*x^2+4*x-6)=0

Step 1 :

Equation at the end of step 1 :

  px-(((((0-(3•(x⁵)))+(4•(x³)))-5x²)+4x)-6)  = 0 
 Step  2  :

Equation at the end of step 2 :

  px-(((((0-(3•(x⁵)))+2²x³)-5x²)+4x)-6)  = 0 
 Step  3  :

Equation at the end of step 3 :

  px-(((((0-3x⁵)+2²x³)-5x²)+4x)-6)  = 0

Step 4 :

Trying to factor by pulling out :

4.1 Factoring: px+3x⁵-4x³+5x²-4x+6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: px+5x²
Group 2: -4x³+3x⁵
Group 3: -4x+6

Pull out from each group separately :

Group 1: (p+5x) • (x)
Group 2: (3x²-4) • (x³)
Group 3: (2x-3) • (-2)

Looking for common sub-expressions :

Group 1: (p+5x) • (x)
Group 3: (2x-3) • (-2)
Group 2: (3x²-4) • (x³)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Equation at the end of step 4 :

  px + 3x⁵ - 4x³ + 5x² - 4x + 6  = 0

Step 5 :

Solving a Single Variable Equation :

5.1 Solve px+3x⁵-4x³+5x²-4x+6 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.