3x(x-2)=23

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Solution for 3x(x-2)=23 equation:


Simplifying
3x(x + -2) = 23

Reorder the terms:
3x(-2 + x) = 23
(-2 * 3x + x * 3x) = 23
(-6x + 3x2) = 23

Solving
-6x + 3x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + -6x + 3x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -6x + 3x2 = 0

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

Divide each side by '3'.
-7.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + -2x + 7.666666667 + x2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + -2x + x2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + 7.666666667
-2x + x2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
-2x + x2 = 7.666666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 7.666666667 + 1

Reorder the terms:
1 + -2x + x2 = 7.666666667 + 1

Combine like terms: 7.666666667 + 1 = 8.666666667
1 + -2x + x2 = 8.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8.666666667

Calculate the square root of the right side: 2.943920289

Break this problem into two subproblems by setting 
(x + -1) equal to 2.943920289 and -2.943920289.

Subproblem 1

x + -1 = 2.943920289 Simplifying x + -1 = 2.943920289 Reorder the terms: -1 + x = 2.943920289 Solving -1 + x = 2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.943920289 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.943920289 + 1 x = 2.943920289 + 1 Combine like terms: 2.943920289 + 1 = 3.943920289 x = 3.943920289 Simplifying x = 3.943920289

Subproblem 2

x + -1 = -2.943920289 Simplifying x + -1 = -2.943920289 Reorder the terms: -1 + x = -2.943920289 Solving -1 + x = -2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.943920289 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.943920289 + 1 x = -2.943920289 + 1 Combine like terms: -2.943920289 + 1 = -1.943920289 x = -1.943920289 Simplifying x = -1.943920289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.943920289, -1.943920289}

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