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

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


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

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

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

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

Combine like terms: -4x + 1x = -3x
(-2 + -3x + 2x2) = -1(x + 3)(x + 7)

Reorder the terms:
-2 + -3x + 2x2 = -1(3 + x)(x + 7)

Reorder the terms:
-2 + -3x + 2x2 = -1(3 + x)(7 + x)

Multiply (3 + x) * (7 + x)
-2 + -3x + 2x2 = -1(3(7 + x) + x(7 + x))
-2 + -3x + 2x2 = -1((7 * 3 + x * 3) + x(7 + x))
-2 + -3x + 2x2 = -1((21 + 3x) + x(7 + x))
-2 + -3x + 2x2 = -1(21 + 3x + (7 * x + x * x))
-2 + -3x + 2x2 = -1(21 + 3x + (7x + x2))

Combine like terms: 3x + 7x = 10x
-2 + -3x + 2x2 = -1(21 + 10x + x2)
-2 + -3x + 2x2 = (21 * -1 + 10x * -1 + x2 * -1)
-2 + -3x + 2x2 = (-21 + -10x + -1x2)

Solving
-2 + -3x + 2x2 = -21 + -10x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2 + 21 + -3x + 10x + 2x2 + x2 = -21 + -10x + -1x2 + 21 + 10x + x2

Combine like terms: -2 + 21 = 19
19 + -3x + 10x + 2x2 + x2 = -21 + -10x + -1x2 + 21 + 10x + x2

Combine like terms: -3x + 10x = 7x
19 + 7x + 2x2 + x2 = -21 + -10x + -1x2 + 21 + 10x + x2

Combine like terms: 2x2 + x2 = 3x2
19 + 7x + 3x2 = -21 + -10x + -1x2 + 21 + 10x + x2

Reorder the terms:
19 + 7x + 3x2 = -21 + 21 + -10x + 10x + -1x2 + x2

Combine like terms: -21 + 21 = 0
19 + 7x + 3x2 = 0 + -10x + 10x + -1x2 + x2
19 + 7x + 3x2 = -10x + 10x + -1x2 + x2

Combine like terms: -10x + 10x = 0
19 + 7x + 3x2 = 0 + -1x2 + x2
19 + 7x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
19 + 7x + 3x2 = 0

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

Divide each side by '3'.
6.333333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-6.333333333' to each side of the equation.
6.333333333 + 2.333333333x + -6.333333333 + x2 = 0 + -6.333333333

Reorder the terms:
6.333333333 + -6.333333333 + 2.333333333x + x2 = 0 + -6.333333333

Combine like terms: 6.333333333 + -6.333333333 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -6.333333333
2.333333333x + x2 = 0 + -6.333333333

Combine like terms: 0 + -6.333333333 = -6.333333333
2.333333333x + x2 = -6.333333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -6.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -6.333333333 + 1.361111112

Combine like terms: -6.333333333 + 1.361111112 = -4.972222221
1.361111112 + 2.333333333x + x2 = -4.972222221

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = -4.972222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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