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

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


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

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

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

Multiply (-4 + x) * (4 + x)
-1(-4(4 + x) + x(4 + x)) = (x + -2)(-5x)
-1((4 * -4 + x * -4) + x(4 + x)) = (x + -2)(-5x)
-1((-16 + -4x) + x(4 + x)) = (x + -2)(-5x)
-1(-16 + -4x + (4 * x + x * x)) = (x + -2)(-5x)
-1(-16 + -4x + (4x + x2)) = (x + -2)(-5x)

Combine like terms: -4x + 4x = 0
-1(-16 + 0 + x2) = (x + -2)(-5x)
-1(-16 + x2) = (x + -2)(-5x)
(-16 * -1 + x2 * -1) = (x + -2)(-5x)
(16 + -1x2) = (x + -2)(-5x)

Reorder the terms:
16 + -1x2 = (-2 + x)(-5x)

Remove parenthesis around (-5x)
16 + -1x2 = (-2 + x) * -5x

Reorder the terms for easier multiplication:
16 + -1x2 = -5x(-2 + x)
16 + -1x2 = (-2 * -5x + x * -5x)
16 + -1x2 = (10x + -5x2)

Solving
16 + -1x2 = 10x + -5x2

Solving for variable 'x'.

Reorder the terms:
16 + -10x + -1x2 + 5x2 = 10x + -5x2 + -10x + 5x2

Combine like terms: -1x2 + 5x2 = 4x2
16 + -10x + 4x2 = 10x + -5x2 + -10x + 5x2

Reorder the terms:
16 + -10x + 4x2 = 10x + -10x + -5x2 + 5x2

Combine like terms: 10x + -10x = 0
16 + -10x + 4x2 = 0 + -5x2 + 5x2
16 + -10x + 4x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
16 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -5x + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + -5x + 2x2 = 0

Solving
8 + -5x + 2x2 = 0

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

Divide each side by '2'.
4 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -2.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2.5x + x2 = 0 + -4
-2.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2.5x + x2 = -4

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -4 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -4 + 1.5625

Combine like terms: -4 + 1.5625 = -2.4375
1.5625 + -2.5x + x2 = -2.4375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = -2.4375

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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