(2x+1)*(2x+3)+7+3=

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Solution for (2x+1)*(2x+3)+7+3= equation: 


Simplifying
(2x + 1)(2x + 3) + 7 + 3 = 0

Reorder the terms:
(1 + 2x)(2x + 3) + 7 + 3 = 0

Reorder the terms:
(1 + 2x)(3 + 2x) + 7 + 3 = 0

Multiply (1 + 2x) * (3 + 2x)
(1(3 + 2x) + 2x * (3 + 2x)) + 7 + 3 = 0
((3 * 1 + 2x * 1) + 2x * (3 + 2x)) + 7 + 3 = 0
((3 + 2x) + 2x * (3 + 2x)) + 7 + 3 = 0
(3 + 2x + (3 * 2x + 2x * 2x)) + 7 + 3 = 0
(3 + 2x + (6x + 4x2)) + 7 + 3 = 0

Combine like terms: 2x + 6x = 8x
(3 + 8x + 4x2) + 7 + 3 = 0

Reorder the terms:
3 + 7 + 3 + 8x + 4x2 = 0

Combine like terms: 3 + 7 = 10
10 + 3 + 8x + 4x2 = 0

Combine like terms: 10 + 3 = 13
13 + 8x + 4x2 = 0

Solving
13 + 8x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
3.25 + 2x + x2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + 2x + -3.25 + x2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + 2x + x2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + 2x + x2 = 0 + -3.25
2x + x2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
2x + x2 = -3.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -3.25 + 1

Reorder the terms:
1 + 2x + x2 = -3.25 + 1

Combine like terms: -3.25 + 1 = -2.25
1 + 2x + x2 = -2.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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