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

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


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

Reorder the terms:
3(3 + 4x) = 2x(3 + -1x) + 2
(3 * 3 + 4x * 3) = 2x(3 + -1x) + 2
(9 + 12x) = 2x(3 + -1x) + 2
9 + 12x = (3 * 2x + -1x * 2x) + 2
9 + 12x = (6x + -2x2) + 2

Reorder the terms:
9 + 12x = 2 + 6x + -2x2

Solving
9 + 12x = 2 + 6x + -2x2

Solving for variable 'x'.

Reorder the terms:
9 + -2 + 12x + -6x + 2x2 = 2 + 6x + -2x2 + -2 + -6x + 2x2

Combine like terms: 9 + -2 = 7
7 + 12x + -6x + 2x2 = 2 + 6x + -2x2 + -2 + -6x + 2x2

Combine like terms: 12x + -6x = 6x
7 + 6x + 2x2 = 2 + 6x + -2x2 + -2 + -6x + 2x2

Reorder the terms:
7 + 6x + 2x2 = 2 + -2 + 6x + -6x + -2x2 + 2x2

Combine like terms: 2 + -2 = 0
7 + 6x + 2x2 = 0 + 6x + -6x + -2x2 + 2x2
7 + 6x + 2x2 = 6x + -6x + -2x2 + 2x2

Combine like terms: 6x + -6x = 0
7 + 6x + 2x2 = 0 + -2x2 + 2x2
7 + 6x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
7 + 6x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 3x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 3x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 3x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 3x + x2 = 0 + -3.5
3x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
3x + x2 = -3.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -3.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -3.5 + 2.25

Combine like terms: -3.5 + 2.25 = -1.25
2.25 + 3x + x2 = -1.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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