3x(4-2x)=5x+10

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Solution for 3x(4-2x)=5x+10 equation:


Simplifying
3x(4 + -2x) = 5x + 10
(4 * 3x + -2x * 3x) = 5x + 10
(12x + -6x2) = 5x + 10

Reorder the terms:
12x + -6x2 = 10 + 5x

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

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + -5x + -6x2 = 10 + 5x + -10 + -5x

Combine like terms: 12x + -5x = 7x
-10 + 7x + -6x2 = 10 + 5x + -10 + -5x

Reorder the terms:
-10 + 7x + -6x2 = 10 + -10 + 5x + -5x

Combine like terms: 10 + -10 = 0
-10 + 7x + -6x2 = 0 + 5x + -5x
-10 + 7x + -6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-10 + 7x + -6x2 = 0

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

Divide each side by '-6'.
1.666666667 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.166666667x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1.166666667x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1.166666667x + x2 = 0 + -1.666666667
-1.166666667x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1.166666667x + x2 = -1.666666667

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 = -1.666666667 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = -1.666666667 + 0.3402777780

Combine like terms: -1.666666667 + 0.3402777780 = -1.326388889
0.3402777780 + -1.166666667x + x2 = -1.326388889

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = -1.326388889

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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