-3x(x-6)=4(2x+3)

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Solution for -3x(x-6)=4(2x+3) equation: 


Simplifying
-3x(x + -6) = 4(2x + 3)

Reorder the terms:
-3x(-6 + x) = 4(2x + 3)
(-6 * -3x + x * -3x) = 4(2x + 3)
(18x + -3x2) = 4(2x + 3)

Reorder the terms:
18x + -3x2 = 4(3 + 2x)
18x + -3x2 = (3 * 4 + 2x * 4)
18x + -3x2 = (12 + 8x)

Solving
18x + -3x2 = 12 + 8x

Solving for variable 'x'.

Reorder the terms:
-12 + 18x + -8x + -3x2 = 12 + 8x + -12 + -8x

Combine like terms: 18x + -8x = 10x
-12 + 10x + -3x2 = 12 + 8x + -12 + -8x

Reorder the terms:
-12 + 10x + -3x2 = 12 + -12 + 8x + -8x

Combine like terms: 12 + -12 = 0
-12 + 10x + -3x2 = 0 + 8x + -8x
-12 + 10x + -3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-12 + 10x + -3x2 = 0

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

Divide each side by '-3'.
4 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -3.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -3.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3.333333333x + x2 = 0 + -4
-3.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3.333333333x + x2 = -4

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -4 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -4 + 2.777777779

Combine like terms: -4 + 2.777777779 = -1.222222221
2.777777779 + -3.333333333x + x2 = -1.222222221

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -1.222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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