3x(2x+4)=10

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Solution for 3x(2x+4)=10 equation: 


Simplifying
3x(2x + 4) = 10

Reorder the terms:
3x(4 + 2x) = 10
(4 * 3x + 2x * 3x) = 10
(12x + 6x2) = 10

Solving
12x + 6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + 6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 6x + 3x2 = 0

Solving
-5 + 6x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.666666667
2x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2x + x2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + 2x + x2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + 2x + x2 = 2.666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + 1) equal to 1.632993162 and -1.632993162.


Subproblem 1
x + 1 = 1.632993162

Simplifying
x + 1 = 1.632993162

Reorder the terms:
1 + x = 1.632993162

Solving
1 + x = 1.632993162

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 = 1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.632993162 + -1
x = 1.632993162 + -1

Combine like terms: 1.632993162 + -1 = 0.632993162
x = 0.632993162

Simplifying
x = 0.632993162


Subproblem 2
x + 1 = -1.632993162

Simplifying
x + 1 = -1.632993162

Reorder the terms:
1 + x = -1.632993162

Solving
1 + x = -1.632993162

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 = -1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.632993162 + -1
x = -1.632993162 + -1

Combine like terms: -1.632993162 + -1 = -2.632993162
x = -2.632993162

Simplifying
x = -2.632993162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.632993162, -2.632993162}
Solution
x = {0.632993162, -2.632993162}

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