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

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


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

Reorder the terms:
2x(3 + x) = (x + 5)(x + -2)
(3 * 2x + x * 2x) = (x + 5)(x + -2)
(6x + 2x2) = (x + 5)(x + -2)

Reorder the terms:
6x + 2x2 = (5 + x)(x + -2)

Reorder the terms:
6x + 2x2 = (5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
6x + 2x2 = (5(-2 + x) + x(-2 + x))
6x + 2x2 = ((-2 * 5 + x * 5) + x(-2 + x))
6x + 2x2 = ((-10 + 5x) + x(-2 + x))
6x + 2x2 = (-10 + 5x + (-2 * x + x * x))
6x + 2x2 = (-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
6x + 2x2 = (-10 + 3x + x2)

Solving
6x + 2x2 = -10 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
10 + 6x + -3x + 2x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Combine like terms: 6x + -3x = 3x
10 + 3x + 2x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 3x + x2 = 0 + -10

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

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

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -10 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + 3x + x2 = -7.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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