4x(x+1)=8(x-4)

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Solution for 4x(x+1)=8(x-4) equation: 


Simplifying
4x(x + 1) = 8(x + -4)

Reorder the terms:
4x(1 + x) = 8(x + -4)
(1 * 4x + x * 4x) = 8(x + -4)
(4x + 4x2) = 8(x + -4)

Reorder the terms:
4x + 4x2 = 8(-4 + x)
4x + 4x2 = (-4 * 8 + x * 8)
4x + 4x2 = (-32 + 8x)

Solving
4x + 4x2 = -32 + 8x

Solving for variable 'x'.

Reorder the terms:
32 + 4x + -8x + 4x2 = -32 + 8x + 32 + -8x

Combine like terms: 4x + -8x = -4x
32 + -4x + 4x2 = -32 + 8x + 32 + -8x

Reorder the terms:
32 + -4x + 4x2 = -32 + 32 + 8x + -8x

Combine like terms: -32 + 32 = 0
32 + -4x + 4x2 = 0 + 8x + -8x
32 + -4x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
32 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -1x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x + x2 = 0

Solving
8 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -1x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -1x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x + x2 = 0 + -8
-1x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x + x2 = -8

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -8 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -8 + 0.25

Combine like terms: -8 + 0.25 = -7.75
0.25 + -1x + x2 = -7.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -7.75

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.

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