(x-1)(x+1)+3-2x=3x+(x-1)*3

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


Simplifying
(x + -1)(x + 1) + 3 + -2x = 3x + (x + -1) * 3

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

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

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3
((1 * -1 + x * -1) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3
((-1 + -1x) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3
(-1 + -1x + (1 * x + x * x)) + 3 + -2x = 3x + (x + -1) * 3
(-1 + -1x + (1x + x2)) + 3 + -2x = 3x + (x + -1) * 3

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) + 3 + -2x = 3x + (x + -1) * 3
(-1 + x2) + 3 + -2x = 3x + (x + -1) * 3

Reorder the terms:
-1 + 3 + -2x + x2 = 3x + (x + -1) * 3

Combine like terms: -1 + 3 = 2
2 + -2x + x2 = 3x + (x + -1) * 3

Reorder the terms:
2 + -2x + x2 = 3x + (-1 + x) * 3

Reorder the terms for easier multiplication:
2 + -2x + x2 = 3x + 3(-1 + x)
2 + -2x + x2 = 3x + (-1 * 3 + x * 3)
2 + -2x + x2 = 3x + (-3 + 3x)

Reorder the terms:
2 + -2x + x2 = -3 + 3x + 3x

Combine like terms: 3x + 3x = 6x
2 + -2x + x2 = -3 + 6x

Solving
2 + -2x + x2 = -3 + 6x

Solving for variable 'x'.

Reorder the terms:
2 + 3 + -2x + -6x + x2 = -3 + 6x + 3 + -6x

Combine like terms: 2 + 3 = 5
5 + -2x + -6x + x2 = -3 + 6x + 3 + -6x

Combine like terms: -2x + -6x = -8x
5 + -8x + x2 = -3 + 6x + 3 + -6x

Reorder the terms:
5 + -8x + x2 = -3 + 3 + 6x + -6x

Combine like terms: -3 + 3 = 0
5 + -8x + x2 = 0 + 6x + -6x
5 + -8x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
5 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x + x2 = 0 + -5
-8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x + x2 = -5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + -8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x + x2 = 11

Factor a perfect square on the left side:
(x + -4)(x + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479

Subproblem 2

x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}

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