(X^2+X-3)*3=(2X-8)*(2X+5)

Solution for (X^2+X-3)*3=(2X-8)*(2X+5) equation:

Simplifying
(X2 + X + -3) * 3 = (2X + -8)(2X + 5)

Reorder the terms:
(-3 + X + X2) * 3 = (2X + -8)(2X + 5)

Reorder the terms for easier multiplication:
3(-3 + X + X2) = (2X + -8)(2X + 5)
(-3 * 3 + X * 3 + X2 * 3) = (2X + -8)(2X + 5)
(-9 + 3X + 3X2) = (2X + -8)(2X + 5)

Reorder the terms:
-9 + 3X + 3X2 = (-8 + 2X)(2X + 5)

Reorder the terms:
-9 + 3X + 3X2 = (-8 + 2X)(5 + 2X)

Multiply (-8 + 2X) * (5 + 2X)
-9 + 3X + 3X2 = (-8(5 + 2X) + 2X * (5 + 2X))
-9 + 3X + 3X2 = ((5 * -8 + 2X * -8) + 2X * (5 + 2X))
-9 + 3X + 3X2 = ((-40 + -16X) + 2X * (5 + 2X))
-9 + 3X + 3X2 = (-40 + -16X + (5 * 2X + 2X * 2X))
-9 + 3X + 3X2 = (-40 + -16X + (10X + 4X2))

Combine like terms: -16X + 10X = -6X
-9 + 3X + 3X2 = (-40 + -6X + 4X2)

Solving
-9 + 3X + 3X2 = -40 + -6X + 4X2

Solving for variable 'X'.

Reorder the terms:
-9 + 40 + 3X + 6X + 3X2 + -4X2 = -40 + -6X + 4X2 + 40 + 6X + -4X2

Combine like terms: -9 + 40 = 31
31 + 3X + 6X + 3X2 + -4X2 = -40 + -6X + 4X2 + 40 + 6X + -4X2

Combine like terms: 3X + 6X = 9X
31 + 9X + 3X2 + -4X2 = -40 + -6X + 4X2 + 40 + 6X + -4X2

Combine like terms: 3X2 + -4X2 = -1X2
31 + 9X + -1X2 = -40 + -6X + 4X2 + 40 + 6X + -4X2

Reorder the terms:
31 + 9X + -1X2 = -40 + 40 + -6X + 6X + 4X2 + -4X2

Combine like terms: -40 + 40 = 0
31 + 9X + -1X2 = 0 + -6X + 6X + 4X2 + -4X2
31 + 9X + -1X2 = -6X + 6X + 4X2 + -4X2

Combine like terms: -6X + 6X = 0
31 + 9X + -1X2 = 0 + 4X2 + -4X2
31 + 9X + -1X2 = 4X2 + -4X2

Combine like terms: 4X2 + -4X2 = 0
31 + 9X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-31 + -9X + X2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -9X + 31 + X2 = 0 + 31

Reorder the terms:
-31 + 31 + -9X + X2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -9X + X2 = 0 + 31
-9X + X2 = 0 + 31

Combine like terms: 0 + 31 = 31
-9X + X2 = 31

The X term is -9X.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9X + 20.25 + X2 = 31 + 20.25

Reorder the terms:
20.25 + -9X + X2 = 31 + 20.25

Combine like terms: 31 + 20.25 = 51.25
20.25 + -9X + X2 = 51.25

Factor a perfect square on the left side:
(X + -4.5)(X + -4.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(X + -4.5) equal to 7.158910532 and -7.158910532.

Subproblem 1
X + -4.5 = 7.158910532

Simplifying
X + -4.5 = 7.158910532

Reorder the terms:
-4.5 + X = 7.158910532

Solving
-4.5 + X = 7.158910532

Solving for variable 'X'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + X = 7.158910532 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = 7.158910532 + 4.5
X = 7.158910532 + 4.5

Combine like terms: 7.158910532 + 4.5 = 11.658910532
X = 11.658910532

Simplifying
X = 11.658910532

Subproblem 2
X + -4.5 = -7.158910532

Simplifying
X + -4.5 = -7.158910532

Reorder the terms:
-4.5 + X = -7.158910532

Solving
-4.5 + X = -7.158910532

Solving for variable 'X'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + X = -7.158910532 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = -7.158910532 + 4.5
X = -7.158910532 + 4.5

Combine like terms: -7.158910532 + 4.5 = -2.658910532
X = -2.658910532

Simplifying
X = -2.658910532

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {11.658910532, -2.658910532}