2(x)(3x-2)=3x+6

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Solution for 2(x)(3x-2)=3x+6 equation:


Simplifying
2(x)(3x + -2) = 3x + 6

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

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

Solving
-4x + 6x2 = 6 + 3x

Solving for variable 'x'.

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

Combine like terms: -4x + -3x = -7x
-6 + -7x + 6x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-6 + -7x + 6x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-6 + -7x + 6x2 = 0 + 3x + -3x
-6 + -7x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + -7x + 6x2 = 0

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

Divide each side by '6'.
-1 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.166666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.166666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.166666667x + x2 = 0 + 1
-1.166666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.166666667x + x2 = 1

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 1 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 1 + 0.3402777780

Combine like terms: 1 + 0.3402777780 = 1.340277778
0.3402777780 + -1.166666667x + x2 = 1.340277778

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 1.340277778

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 1.157703666 and -1.157703666.

Subproblem 1

x + -0.5833333335 = 1.157703666 Simplifying x + -0.5833333335 = 1.157703666 Reorder the terms: -0.5833333335 + x = 1.157703666 Solving -0.5833333335 + x = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.157703666 + 0.5833333335 x = 1.157703666 + 0.5833333335 Combine like terms: 1.157703666 + 0.5833333335 = 1.7410369995 x = 1.7410369995 Simplifying x = 1.7410369995

Subproblem 2

x + -0.5833333335 = -1.157703666 Simplifying x + -0.5833333335 = -1.157703666 Reorder the terms: -0.5833333335 + x = -1.157703666 Solving -0.5833333335 + x = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.157703666 + 0.5833333335 x = -1.157703666 + 0.5833333335 Combine like terms: -1.157703666 + 0.5833333335 = -0.5743703325 x = -0.5743703325 Simplifying x = -0.5743703325

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7410369995, -0.5743703325}

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