3x(x-2)=4

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Solution for 3x(x-2)=4 equation:


Simplifying
3x(x + -2) = 4

Reorder the terms:
3x(-2 + x) = 4
(-2 * 3x + x * 3x) = 4
(-6x + 3x2) = 4

Solving
-6x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -6x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.333333333
-2x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2x + x2 = 1.333333333

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 = 1.333333333 + 1

Reorder the terms:
1 + -2x + x2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + -2x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -1) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + -1 = 1.527525232 Simplifying x + -1 = 1.527525232 Reorder the terms: -1 + x = 1.527525232 Solving -1 + x = 1.527525232 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 = 1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.527525232 + 1 x = 1.527525232 + 1 Combine like terms: 1.527525232 + 1 = 2.527525232 x = 2.527525232 Simplifying x = 2.527525232

Subproblem 2

x + -1 = -1.527525232 Simplifying x + -1 = -1.527525232 Reorder the terms: -1 + x = -1.527525232 Solving -1 + x = -1.527525232 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 = -1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.527525232 + 1 x = -1.527525232 + 1 Combine like terms: -1.527525232 + 1 = -0.527525232 x = -0.527525232 Simplifying x = -0.527525232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.527525232, -0.527525232}

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