4x(x+1)=(x+2)(x-5)

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Solution for 4x(x+1)=(x+2)(x-5) equation: 


Simplifying
4x(x + 1) = (x + 2)(x + -5)

Reorder the terms:
4x(1 + x) = (x + 2)(x + -5)
(1 * 4x + x * 4x) = (x + 2)(x + -5)
(4x + 4x2) = (x + 2)(x + -5)

Reorder the terms:
4x + 4x2 = (2 + x)(x + -5)

Reorder the terms:
4x + 4x2 = (2 + x)(-5 + x)

Multiply (2 + x) * (-5 + x)
4x + 4x2 = (2(-5 + x) + x(-5 + x))
4x + 4x2 = ((-5 * 2 + x * 2) + x(-5 + x))
4x + 4x2 = ((-10 + 2x) + x(-5 + x))
4x + 4x2 = (-10 + 2x + (-5 * x + x * x))
4x + 4x2 = (-10 + 2x + (-5x + x2))

Combine like terms: 2x + -5x = -3x
4x + 4x2 = (-10 + -3x + x2)

Solving
4x + 4x2 = -10 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
10 + 4x + 3x + 4x2 + -1x2 = -10 + -3x + x2 + 10 + 3x + -1x2

Combine like terms: 4x + 3x = 7x
10 + 7x + 4x2 + -1x2 = -10 + -3x + x2 + 10 + 3x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
10 + 7x + 3x2 = -10 + -3x + x2 + 10 + 3x + -1x2

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

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

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

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

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

Divide each side by '3'.
3.333333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 2.333333333x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 2.333333333x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -3.333333333
2.333333333x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
2.333333333x + x2 = -3.333333333

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 = -3.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -3.333333333 + 1.361111112

Combine like terms: -3.333333333 + 1.361111112 = -1.972222221
1.361111112 + 2.333333333x + x2 = -1.972222221

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = -1.972222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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