(2x+1)(x+5)+(2x-1)(x-2)=0

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Solution for (2x+1)(x+5)+(2x-1)(x-2)=0 equation: 


Simplifying
(2x + 1)(x + 5) + (2x + -1)(x + -2) = 0

Reorder the terms:
(1 + 2x)(x + 5) + (2x + -1)(x + -2) = 0

Reorder the terms:
(1 + 2x)(5 + x) + (2x + -1)(x + -2) = 0

Multiply (1 + 2x) * (5 + x)
(1(5 + x) + 2x * (5 + x)) + (2x + -1)(x + -2) = 0
((5 * 1 + x * 1) + 2x * (5 + x)) + (2x + -1)(x + -2) = 0
((5 + 1x) + 2x * (5 + x)) + (2x + -1)(x + -2) = 0
(5 + 1x + (5 * 2x + x * 2x)) + (2x + -1)(x + -2) = 0
(5 + 1x + (10x + 2x2)) + (2x + -1)(x + -2) = 0

Combine like terms: 1x + 10x = 11x
(5 + 11x + 2x2) + (2x + -1)(x + -2) = 0

Reorder the terms:
5 + 11x + 2x2 + (-1 + 2x)(x + -2) = 0

Reorder the terms:
5 + 11x + 2x2 + (-1 + 2x)(-2 + x) = 0

Multiply (-1 + 2x) * (-2 + x)
5 + 11x + 2x2 + (-1(-2 + x) + 2x * (-2 + x)) = 0
5 + 11x + 2x2 + ((-2 * -1 + x * -1) + 2x * (-2 + x)) = 0
5 + 11x + 2x2 + ((2 + -1x) + 2x * (-2 + x)) = 0
5 + 11x + 2x2 + (2 + -1x + (-2 * 2x + x * 2x)) = 0
5 + 11x + 2x2 + (2 + -1x + (-4x + 2x2)) = 0

Combine like terms: -1x + -4x = -5x
5 + 11x + 2x2 + (2 + -5x + 2x2) = 0

Reorder the terms:
5 + 2 + 11x + -5x + 2x2 + 2x2 = 0

Combine like terms: 5 + 2 = 7
7 + 11x + -5x + 2x2 + 2x2 = 0

Combine like terms: 11x + -5x = 6x
7 + 6x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
7 + 6x + 4x2 = 0

Solving
7 + 6x + 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'.
1.75 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 1.5x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 1.5x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 1.5x + x2 = 0 + -1.75
1.5x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
1.5x + x2 = -1.75

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -1.75 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -1.75 + 0.5625

Combine like terms: -1.75 + 0.5625 = -1.1875
0.5625 + 1.5x + x2 = -1.1875

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -1.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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