(x-3)(4-x)=15

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Solution for (x-3)(4-x)=15 equation: 


Simplifying
(x + -3)(4 + -1x) = 15

Reorder the terms:
(-3 + x)(4 + -1x) = 15

Multiply (-3 + x) * (4 + -1x)
(-3(4 + -1x) + x(4 + -1x)) = 15
((4 * -3 + -1x * -3) + x(4 + -1x)) = 15
((-12 + 3x) + x(4 + -1x)) = 15
(-12 + 3x + (4 * x + -1x * x)) = 15
(-12 + 3x + (4x + -1x2)) = 15

Combine like terms: 3x + 4x = 7x
(-12 + 7x + -1x2) = 15

Solving
-12 + 7x + -1x2 = 15

Solving for variable 'x'.

Reorder the terms:
-12 + -15 + 7x + -1x2 = 15 + -15

Combine like terms: -12 + -15 = -27
-27 + 7x + -1x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-27 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
27 + -7x + x2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -7x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -7x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -7x + x2 = 0 + -27
-7x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-7x + x2 = -27

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -27 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -27 + 12.25

Combine like terms: -27 + 12.25 = -14.75
12.25 + -7x + x2 = -14.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = -14.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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