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

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

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

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

Reorder the terms:
2x + 2x2 = 5(-4 + x)
2x + 2x2 = (-4 * 5 + x * 5)
2x + 2x2 = (-20 + 5x)

Solving
2x + 2x2 = -20 + 5x

Solving for variable 'x'.

Reorder the terms:
20 + 2x + -5x + 2x2 = -20 + 5x + 20 + -5x

Combine like terms: 2x + -5x = -3x
20 + -3x + 2x2 = -20 + 5x + 20 + -5x

Reorder the terms:
20 + -3x + 2x2 = -20 + 20 + 5x + -5x

Combine like terms: -20 + 20 = 0
20 + -3x + 2x2 = 0 + 5x + -5x
20 + -3x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
20 + -3x + 2x2 = 0

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

Divide each side by '2'.
10 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -1.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -1.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1.5x + x2 = 0 + -10
-1.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1.5x + x2 = -10

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 = -10 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -10 + 0.5625

Combine like terms: -10 + 0.5625 = -9.4375
0.5625 + -1.5x + x2 = -9.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -9.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.