(3x-4)(-2x+7)=9

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Solution for (3x-4)(-2x+7)=9 equation: 


Simplifying
(3x + -4)(-2x + 7) = 9

Reorder the terms:
(-4 + 3x)(-2x + 7) = 9

Reorder the terms:
(-4 + 3x)(7 + -2x) = 9

Multiply (-4 + 3x) * (7 + -2x)
(-4(7 + -2x) + 3x * (7 + -2x)) = 9
((7 * -4 + -2x * -4) + 3x * (7 + -2x)) = 9
((-28 + 8x) + 3x * (7 + -2x)) = 9
(-28 + 8x + (7 * 3x + -2x * 3x)) = 9
(-28 + 8x + (21x + -6x2)) = 9

Combine like terms: 8x + 21x = 29x
(-28 + 29x + -6x2) = 9

Solving
-28 + 29x + -6x2 = 9

Solving for variable 'x'.

Reorder the terms:
-28 + -9 + 29x + -6x2 = 9 + -9

Combine like terms: -28 + -9 = -37
-37 + 29x + -6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-37 + 29x + -6x2 = 0

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

Divide each side by '-6'.
6.166666667 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '-6.166666667' to each side of the equation.
6.166666667 + -4.833333333x + -6.166666667 + x2 = 0 + -6.166666667

Reorder the terms:
6.166666667 + -6.166666667 + -4.833333333x + x2 = 0 + -6.166666667

Combine like terms: 6.166666667 + -6.166666667 = 0.000000000
0.000000000 + -4.833333333x + x2 = 0 + -6.166666667
-4.833333333x + x2 = 0 + -6.166666667

Combine like terms: 0 + -6.166666667 = -6.166666667
-4.833333333x + x2 = -6.166666667

The x term is -4.833333333x.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333x + 5.840277779 + x2 = -6.166666667 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = -6.166666667 + 5.840277779

Combine like terms: -6.166666667 + 5.840277779 = -0.326388888
5.840277779 + -4.833333333x + x2 = -0.326388888

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = -0.326388888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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