3(4+2x)=5x(x-2)

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Solution for 3(4+2x)=5x(x-2) equation:


Simplifying
3(4 + 2x) = 5x(x + -2)
(4 * 3 + 2x * 3) = 5x(x + -2)
(12 + 6x) = 5x(x + -2)

Reorder the terms:
12 + 6x = 5x(-2 + x)
12 + 6x = (-2 * 5x + x * 5x)
12 + 6x = (-10x + 5x2)

Solving
12 + 6x = -10x + 5x2

Solving for variable 'x'.

Combine like terms: 6x + 10x = 16x
12 + 16x + -5x2 = -10x + 5x2 + 10x + -5x2

Reorder the terms:
12 + 16x + -5x2 = -10x + 10x + 5x2 + -5x2

Combine like terms: -10x + 10x = 0
12 + 16x + -5x2 = 0 + 5x2 + -5x2
12 + 16x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
12 + 16x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.4 + -3.2x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -3.2x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -3.2x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -3.2x + x2 = 0 + 2.4
-3.2x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-3.2x + x2 = 2.4

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = 2.4 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 2.4 + 2.56

Combine like terms: 2.4 + 2.56 = 4.96
2.56 + -3.2x + x2 = 4.96

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 4.96

Calculate the square root of the right side: 2.227105745

Break this problem into two subproblems by setting 
(x + -1.6) equal to 2.227105745 and -2.227105745.

Subproblem 1

x + -1.6 = 2.227105745 Simplifying x + -1.6 = 2.227105745 Reorder the terms: -1.6 + x = 2.227105745 Solving -1.6 + x = 2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.227105745 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.227105745 + 1.6 x = 2.227105745 + 1.6 Combine like terms: 2.227105745 + 1.6 = 3.827105745 x = 3.827105745 Simplifying x = 3.827105745

Subproblem 2

x + -1.6 = -2.227105745 Simplifying x + -1.6 = -2.227105745 Reorder the terms: -1.6 + x = -2.227105745 Solving -1.6 + x = -2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.227105745 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.227105745 + 1.6 x = -2.227105745 + 1.6 Combine like terms: -2.227105745 + 1.6 = -0.627105745 x = -0.627105745 Simplifying x = -0.627105745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.827105745, -0.627105745}

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