(2X-3)(X+1)=X

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Solution for (2X-3)(X+1)=X equation:


Simplifying
(2X + -3)(X + 1) = X

Reorder the terms:
(-3 + 2X)(X + 1) = X

Reorder the terms:
(-3 + 2X)(1 + X) = X

Multiply (-3 + 2X) * (1 + X)
(-3(1 + X) + 2X * (1 + X)) = X
((1 * -3 + X * -3) + 2X * (1 + X)) = X
((-3 + -3X) + 2X * (1 + X)) = X
(-3 + -3X + (1 * 2X + X * 2X)) = X
(-3 + -3X + (2X + 2X2)) = X

Combine like terms: -3X + 2X = -1X
(-3 + -1X + 2X2) = X

Solving
-3 + -1X + 2X2 = X

Solving for variable 'X'.

Reorder the terms:
-3 + -1X + -1X + 2X2 = X + -1X

Combine like terms: -1X + -1X = -2X
-3 + -2X + 2X2 = X + -1X

Combine like terms: X + -1X = 0
-3 + -2X + 2X2 = 0

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

Divide each side by '2'.
-1.5 + -1X + X2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1X + 1.5 + X2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1X + X2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1X + X2 = 0 + 1.5
-1X + X2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1X + X2 = 1.5

The X term is -1X.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1X + 0.25 + X2 = 1.5 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + -1X + X2 = 1.75

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(X + -0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

X + -0.5 = 1.322875656 Simplifying X + -0.5 = 1.322875656 Reorder the terms: -0.5 + X = 1.322875656 Solving -0.5 + X = 1.322875656 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 1.322875656 + 0.5 X = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 X = 1.822875656 Simplifying X = 1.822875656

Subproblem 2

X + -0.5 = -1.322875656 Simplifying X + -0.5 = -1.322875656 Reorder the terms: -0.5 + X = -1.322875656 Solving -0.5 + X = -1.322875656 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -1.322875656 + 0.5 X = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 X = -0.822875656 Simplifying X = -0.822875656

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.822875656, -0.822875656}

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