(x+3)(x+5)=99+x(2x-1)

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Solution for (x+3)(x+5)=99+x(2x-1) equation: 


Simplifying
(x + 3)(x + 5) = 99 + x(2x + -1)

Reorder the terms:
(3 + x)(x + 5) = 99 + x(2x + -1)

Reorder the terms:
(3 + x)(5 + x) = 99 + x(2x + -1)

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = 99 + x(2x + -1)
((5 * 3 + x * 3) + x(5 + x)) = 99 + x(2x + -1)
((15 + 3x) + x(5 + x)) = 99 + x(2x + -1)
(15 + 3x + (5 * x + x * x)) = 99 + x(2x + -1)
(15 + 3x + (5x + x2)) = 99 + x(2x + -1)

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = 99 + x(2x + -1)

Reorder the terms:
15 + 8x + x2 = 99 + x(-1 + 2x)
15 + 8x + x2 = 99 + (-1 * x + 2x * x)
15 + 8x + x2 = 99 + (-1x + 2x2)

Solving
15 + 8x + x2 = 99 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
15 + -99 + 8x + x + x2 + -2x2 = 99 + -1x + 2x2 + -99 + x + -2x2

Combine like terms: 15 + -99 = -84
-84 + 8x + x + x2 + -2x2 = 99 + -1x + 2x2 + -99 + x + -2x2

Combine like terms: 8x + x = 9x
-84 + 9x + x2 + -2x2 = 99 + -1x + 2x2 + -99 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-84 + 9x + -1x2 = 99 + -1x + 2x2 + -99 + x + -2x2

Reorder the terms:
-84 + 9x + -1x2 = 99 + -99 + -1x + x + 2x2 + -2x2

Combine like terms: 99 + -99 = 0
-84 + 9x + -1x2 = 0 + -1x + x + 2x2 + -2x2
-84 + 9x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-84 + 9x + -1x2 = 0 + 2x2 + -2x2
-84 + 9x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-84 + 9x + -1x2 = 0

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

Divide each side by '-1'.
84 + -9x + x2 = 0

Move the constant term to the right:

Add '-84' to each side of the equation.
84 + -9x + -84 + x2 = 0 + -84

Reorder the terms:
84 + -84 + -9x + x2 = 0 + -84

Combine like terms: 84 + -84 = 0
0 + -9x + x2 = 0 + -84
-9x + x2 = 0 + -84

Combine like terms: 0 + -84 = -84
-9x + x2 = -84

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -84 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -84 + 20.25

Combine like terms: -84 + 20.25 = -63.75
20.25 + -9x + x2 = -63.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = -63.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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