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

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

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

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

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

Multiply (-1a + x) * (-4 + x)
4(-1a * (-4 + x) + x(-4 + x)) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
4((-4 * -1a + x * -1a) + x(-4 + x)) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
4((4a + -1ax) + x(-4 + x)) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
4(4a + -1ax + (-4 * x + x * x)) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
4(4a + -1ax + (-4x + x2)) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
4(4a + -1ax + -4x + x2) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
(4a * 4 + -1ax * 4 + -4x * 4 + x2 * 4) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)
(16a + -4ax + -16x + 4x2) + 4(x + -1a)(x + -4) = 8(x + -1a)(x + a)

Reorder the terms:
16a + -4ax + -16x + 4x2 + 4(-1a + x)(x + -4) = 8(x + -1a)(x + a)

Reorder the terms:
16a + -4ax + -16x + 4x2 + 4(-1a + x)(-4 + x) = 8(x + -1a)(x + a)

Multiply (-1a + x) * (-4 + x)
16a + -4ax + -16x + 4x2 + 4(-1a * (-4 + x) + x(-4 + x)) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + 4((-4 * -1a + x * -1a) + x(-4 + x)) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + 4((4a + -1ax) + x(-4 + x)) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + 4(4a + -1ax + (-4 * x + x * x)) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + 4(4a + -1ax + (-4x + x2)) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + 4(4a + -1ax + -4x + x2) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + (4a * 4 + -1ax * 4 + -4x * 4 + x2 * 4) = 8(x + -1a)(x + a)
16a + -4ax + -16x + 4x2 + (16a + -4ax + -16x + 4x2) = 8(x + -1a)(x + a)

Reorder the terms:
16a + 16a + -4ax + -4ax + -16x + -16x + 4x2 + 4x2 = 8(x + -1a)(x + a)

Combine like terms: 16a + 16a = 32a
32a + -4ax + -4ax + -16x + -16x + 4x2 + 4x2 = 8(x + -1a)(x + a)

Combine like terms: -4ax + -4ax = -8ax
32a + -8ax + -16x + -16x + 4x2 + 4x2 = 8(x + -1a)(x + a)

Combine like terms: -16x + -16x = -32x
32a + -8ax + -32x + 4x2 + 4x2 = 8(x + -1a)(x + a)

Combine like terms: 4x2 + 4x2 = 8x2
32a + -8ax + -32x + 8x2 = 8(x + -1a)(x + a)

Reorder the terms:
32a + -8ax + -32x + 8x2 = 8(-1a + x)(x + a)

Reorder the terms:
32a + -8ax + -32x + 8x2 = 8(-1a + x)(a + x)

Multiply (-1a + x) * (a + x)
32a + -8ax + -32x + 8x2 = 8(-1a * (a + x) + x(a + x))
32a + -8ax + -32x + 8x2 = 8((a * -1a + x * -1a) + x(a + x))

Reorder the terms:
32a + -8ax + -32x + 8x2 = 8((-1ax + -1a2) + x(a + x))
32a + -8ax + -32x + 8x2 = 8((-1ax + -1a2) + x(a + x))
32a + -8ax + -32x + 8x2 = 8(-1ax + -1a2 + (a * x + x * x))
32a + -8ax + -32x + 8x2 = 8(-1ax + -1a2 + (ax + x2))

Reorder the terms:
32a + -8ax + -32x + 8x2 = 8(-1ax + ax + -1a2 + x2)

Combine like terms: -1ax + ax = 0
32a + -8ax + -32x + 8x2 = 8(0 + -1a2 + x2)
32a + -8ax + -32x + 8x2 = 8(-1a2 + x2)
32a + -8ax + -32x + 8x2 = (-1a2 * 8 + x2 * 8)
32a + -8ax + -32x + 8x2 = (-8a2 + 8x2)

Add '-8x2' to each side of the equation.
32a + -8ax + -32x + 8x2 + -8x2 = -8a2 + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
32a + -8ax + -32x + 0 = -8a2 + 8x2 + -8x2
32a + -8ax + -32x = -8a2 + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
32a + -8ax + -32x = -8a2 + 0
32a + -8ax + -32x = -8a2

Solving
32a + -8ax + -32x = -8a2

Solving for variable 'a'.

Reorder the terms:
32a + -8ax + 8a2 + -32x = -8a2 + 8a2

Combine like terms: -8a2 + 8a2 = 0
32a + -8ax + 8a2 + -32x = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4a + -1ax + a2 + -4x) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(4a + -1ax + a2 + -4x)' equal to zero and attempt to solve:

Simplifying
4a + -1ax + a2 + -4x = 0

Solving
4a + -1ax + a2 + -4x = 0

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.