64(x+8)(x+16)+4(x+12)(x+8)=16(x+4)(x+8)

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Solution for 64(x+8)(x+16)+4(x+12)(x+8)=16(x+4)(x+8) equation: 


Simplifying
64(x + 8)(x + 16) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)

Reorder the terms:
64(8 + x)(x + 16) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)

Reorder the terms:
64(8 + x)(16 + x) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)

Multiply (8 + x) * (16 + x)
64(8(16 + x) + x(16 + x)) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
64((16 * 8 + x * 8) + x(16 + x)) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
64((128 + 8x) + x(16 + x)) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
64(128 + 8x + (16 * x + x * x)) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
64(128 + 8x + (16x + x2)) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)

Combine like terms: 8x + 16x = 24x
64(128 + 24x + x2) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
(128 * 64 + 24x * 64 + x2 * 64) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)
(8192 + 1536x + 64x2) + 4(x + 12)(x + 8) = 16(x + 4)(x + 8)

Reorder the terms:
8192 + 1536x + 64x2 + 4(12 + x)(x + 8) = 16(x + 4)(x + 8)

Reorder the terms:
8192 + 1536x + 64x2 + 4(12 + x)(8 + x) = 16(x + 4)(x + 8)

Multiply (12 + x) * (8 + x)
8192 + 1536x + 64x2 + 4(12(8 + x) + x(8 + x)) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + 4((8 * 12 + x * 12) + x(8 + x)) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + 4((96 + 12x) + x(8 + x)) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + 4(96 + 12x + (8 * x + x * x)) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + 4(96 + 12x + (8x + x2)) = 16(x + 4)(x + 8)

Combine like terms: 12x + 8x = 20x
8192 + 1536x + 64x2 + 4(96 + 20x + x2) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + (96 * 4 + 20x * 4 + x2 * 4) = 16(x + 4)(x + 8)
8192 + 1536x + 64x2 + (384 + 80x + 4x2) = 16(x + 4)(x + 8)

Reorder the terms:
8192 + 384 + 1536x + 80x + 64x2 + 4x2 = 16(x + 4)(x + 8)

Combine like terms: 8192 + 384 = 8576
8576 + 1536x + 80x + 64x2 + 4x2 = 16(x + 4)(x + 8)

Combine like terms: 1536x + 80x = 1616x
8576 + 1616x + 64x2 + 4x2 = 16(x + 4)(x + 8)

Combine like terms: 64x2 + 4x2 = 68x2
8576 + 1616x + 68x2 = 16(x + 4)(x + 8)

Reorder the terms:
8576 + 1616x + 68x2 = 16(4 + x)(x + 8)

Reorder the terms:
8576 + 1616x + 68x2 = 16(4 + x)(8 + x)

Multiply (4 + x) * (8 + x)
8576 + 1616x + 68x2 = 16(4(8 + x) + x(8 + x))
8576 + 1616x + 68x2 = 16((8 * 4 + x * 4) + x(8 + x))
8576 + 1616x + 68x2 = 16((32 + 4x) + x(8 + x))
8576 + 1616x + 68x2 = 16(32 + 4x + (8 * x + x * x))
8576 + 1616x + 68x2 = 16(32 + 4x + (8x + x2))

Combine like terms: 4x + 8x = 12x
8576 + 1616x + 68x2 = 16(32 + 12x + x2)
8576 + 1616x + 68x2 = (32 * 16 + 12x * 16 + x2 * 16)
8576 + 1616x + 68x2 = (512 + 192x + 16x2)

Solving
8576 + 1616x + 68x2 = 512 + 192x + 16x2

Solving for variable 'x'.

Reorder the terms:
8576 + -512 + 1616x + -192x + 68x2 + -16x2 = 512 + 192x + 16x2 + -512 + -192x + -16x2

Combine like terms: 8576 + -512 = 8064
8064 + 1616x + -192x + 68x2 + -16x2 = 512 + 192x + 16x2 + -512 + -192x + -16x2

Combine like terms: 1616x + -192x = 1424x
8064 + 1424x + 68x2 + -16x2 = 512 + 192x + 16x2 + -512 + -192x + -16x2

Combine like terms: 68x2 + -16x2 = 52x2
8064 + 1424x + 52x2 = 512 + 192x + 16x2 + -512 + -192x + -16x2

Reorder the terms:
8064 + 1424x + 52x2 = 512 + -512 + 192x + -192x + 16x2 + -16x2

Combine like terms: 512 + -512 = 0
8064 + 1424x + 52x2 = 0 + 192x + -192x + 16x2 + -16x2
8064 + 1424x + 52x2 = 192x + -192x + 16x2 + -16x2

Combine like terms: 192x + -192x = 0
8064 + 1424x + 52x2 = 0 + 16x2 + -16x2
8064 + 1424x + 52x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
8064 + 1424x + 52x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2016 + 356x + 13x2) = 0

Factor a trinomial.
4((252 + 13x)(8 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(252 + 13x)' equal to zero and attempt to solve:

Simplifying
252 + 13x = 0

Solving
252 + 13x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-252' to each side of the equation.
252 + -252 + 13x = 0 + -252

Combine like terms: 252 + -252 = 0
0 + 13x = 0 + -252
13x = 0 + -252

Combine like terms: 0 + -252 = -252
13x = -252

Divide each side by '13'.
x = -19.38461538

Simplifying
x = -19.38461538

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

Simplifying
8 + x = 0

Solving
8 + x = 0

Move all terms containing x to the left, all other terms to the right.

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

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

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

Simplifying
x = -8
Solution
x = {-19.38461538, -8}

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