-4x(x+2)=8(x+5)

Solution for -4x(x+2)=8(x+5) equation:

Simplifying
-4x(x + 2) = 8(x + 5)

Reorder the terms:
-4x(2 + x) = 8(x + 5)
(2 * -4x + x * -4x) = 8(x + 5)
(-8x + -4x2) = 8(x + 5)

Reorder the terms:
-8x + -4x2 = 8(5 + x)
-8x + -4x2 = (5 * 8 + x * 8)
-8x + -4x2 = (40 + 8x)

Solving
-8x + -4x2 = 40 + 8x

Solving for variable 'x'.

Reorder the terms:
-40 + -8x + -8x + -4x2 = 40 + 8x + -40 + -8x

Combine like terms: -8x + -8x = -16x
-40 + -16x + -4x2 = 40 + 8x + -40 + -8x

Reorder the terms:
-40 + -16x + -4x2 = 40 + -40 + 8x + -8x

Combine like terms: 40 + -40 = 0
-40 + -16x + -4x2 = 0 + 8x + -8x
-40 + -16x + -4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-40 + -16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(10 + 4x + x2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(10 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 4x + x2 = 0

Solving
10 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 4x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 4x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 4x + x2 = 0 + -10
4x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
4x + x2 = -10

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -10 + 4

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

Combine like terms: -10 + 4 = -6
4 + 4x + x2 = -6

Factor a perfect square on the left side:
(x + 2)(x + 2) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.