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

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


Simplifying
3x(x + 4) = 2(5 + -1x)

Reorder the terms:
3x(4 + x) = 2(5 + -1x)
(4 * 3x + x * 3x) = 2(5 + -1x)
(12x + 3x2) = 2(5 + -1x)
12x + 3x2 = (5 * 2 + -1x * 2)
12x + 3x2 = (10 + -2x)

Solving
12x + 3x2 = 10 + -2x

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + 2x + 3x2 = 10 + -2x + -10 + 2x

Combine like terms: 12x + 2x = 14x
-10 + 14x + 3x2 = 10 + -2x + -10 + 2x

Reorder the terms:
-10 + 14x + 3x2 = 10 + -10 + -2x + 2x

Combine like terms: 10 + -10 = 0
-10 + 14x + 3x2 = 0 + -2x + 2x
-10 + 14x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-10 + 14x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 4.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 4.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + 3.333333333
4.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
4.666666667x + x2 = 3.333333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 3.333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 3.333333333 + 5.444444448

Combine like terms: 3.333333333 + 5.444444448 = 8.777777781
5.444444448 + 4.666666667x + x2 = 8.777777781

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 8.777777781

Calculate the square root of the right side: 2.962731473

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.962731473 and -2.962731473.

Subproblem 1

x + 2.333333334 = 2.962731473 Simplifying x + 2.333333334 = 2.962731473 Reorder the terms: 2.333333334 + x = 2.962731473 Solving 2.333333334 + x = 2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 2.962731473 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.962731473 + -2.333333334 x = 2.962731473 + -2.333333334 Combine like terms: 2.962731473 + -2.333333334 = 0.629398139 x = 0.629398139 Simplifying x = 0.629398139

Subproblem 2

x + 2.333333334 = -2.962731473 Simplifying x + 2.333333334 = -2.962731473 Reorder the terms: 2.333333334 + x = -2.962731473 Solving 2.333333334 + x = -2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -2.962731473 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.962731473 + -2.333333334 x = -2.962731473 + -2.333333334 Combine like terms: -2.962731473 + -2.333333334 = -5.296064807 x = -5.296064807 Simplifying x = -5.296064807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.629398139, -5.296064807}

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