16(x-5)(x+20)+4(x+12)(x-4)=36(x-3)(x+6)

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Solution for 16(x-5)(x+20)+4(x+12)(x-4)=36(x-3)(x+6) equation: 


Simplifying
16(x + -5)(x + 20) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)

Reorder the terms:
16(-5 + x)(x + 20) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)

Reorder the terms:
16(-5 + x)(20 + x) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)

Multiply (-5 + x) * (20 + x)
16(-5(20 + x) + x(20 + x)) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
16((20 * -5 + x * -5) + x(20 + x)) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
16((-100 + -5x) + x(20 + x)) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
16(-100 + -5x + (20 * x + x * x)) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
16(-100 + -5x + (20x + x2)) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)

Combine like terms: -5x + 20x = 15x
16(-100 + 15x + x2) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
(-100 * 16 + 15x * 16 + x2 * 16) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)
(-1600 + 240x + 16x2) + 4(x + 12)(x + -4) = 36(x + -3)(x + 6)

Reorder the terms:
-1600 + 240x + 16x2 + 4(12 + x)(x + -4) = 36(x + -3)(x + 6)

Reorder the terms:
-1600 + 240x + 16x2 + 4(12 + x)(-4 + x) = 36(x + -3)(x + 6)

Multiply (12 + x) * (-4 + x)
-1600 + 240x + 16x2 + 4(12(-4 + x) + x(-4 + x)) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + 4((-4 * 12 + x * 12) + x(-4 + x)) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + 4((-48 + 12x) + x(-4 + x)) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + 4(-48 + 12x + (-4 * x + x * x)) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + 4(-48 + 12x + (-4x + x2)) = 36(x + -3)(x + 6)

Combine like terms: 12x + -4x = 8x
-1600 + 240x + 16x2 + 4(-48 + 8x + x2) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + (-48 * 4 + 8x * 4 + x2 * 4) = 36(x + -3)(x + 6)
-1600 + 240x + 16x2 + (-192 + 32x + 4x2) = 36(x + -3)(x + 6)

Reorder the terms:
-1600 + -192 + 240x + 32x + 16x2 + 4x2 = 36(x + -3)(x + 6)

Combine like terms: -1600 + -192 = -1792
-1792 + 240x + 32x + 16x2 + 4x2 = 36(x + -3)(x + 6)

Combine like terms: 240x + 32x = 272x
-1792 + 272x + 16x2 + 4x2 = 36(x + -3)(x + 6)

Combine like terms: 16x2 + 4x2 = 20x2
-1792 + 272x + 20x2 = 36(x + -3)(x + 6)

Reorder the terms:
-1792 + 272x + 20x2 = 36(-3 + x)(x + 6)

Reorder the terms:
-1792 + 272x + 20x2 = 36(-3 + x)(6 + x)

Multiply (-3 + x) * (6 + x)
-1792 + 272x + 20x2 = 36(-3(6 + x) + x(6 + x))
-1792 + 272x + 20x2 = 36((6 * -3 + x * -3) + x(6 + x))
-1792 + 272x + 20x2 = 36((-18 + -3x) + x(6 + x))
-1792 + 272x + 20x2 = 36(-18 + -3x + (6 * x + x * x))
-1792 + 272x + 20x2 = 36(-18 + -3x + (6x + x2))

Combine like terms: -3x + 6x = 3x
-1792 + 272x + 20x2 = 36(-18 + 3x + x2)
-1792 + 272x + 20x2 = (-18 * 36 + 3x * 36 + x2 * 36)
-1792 + 272x + 20x2 = (-648 + 108x + 36x2)

Solving
-1792 + 272x + 20x2 = -648 + 108x + 36x2

Solving for variable 'x'.

Reorder the terms:
-1792 + 648 + 272x + -108x + 20x2 + -36x2 = -648 + 108x + 36x2 + 648 + -108x + -36x2

Combine like terms: -1792 + 648 = -1144
-1144 + 272x + -108x + 20x2 + -36x2 = -648 + 108x + 36x2 + 648 + -108x + -36x2

Combine like terms: 272x + -108x = 164x
-1144 + 164x + 20x2 + -36x2 = -648 + 108x + 36x2 + 648 + -108x + -36x2

Combine like terms: 20x2 + -36x2 = -16x2
-1144 + 164x + -16x2 = -648 + 108x + 36x2 + 648 + -108x + -36x2

Reorder the terms:
-1144 + 164x + -16x2 = -648 + 648 + 108x + -108x + 36x2 + -36x2

Combine like terms: -648 + 648 = 0
-1144 + 164x + -16x2 = 0 + 108x + -108x + 36x2 + -36x2
-1144 + 164x + -16x2 = 108x + -108x + 36x2 + -36x2

Combine like terms: 108x + -108x = 0
-1144 + 164x + -16x2 = 0 + 36x2 + -36x2
-1144 + 164x + -16x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
-1144 + 164x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-286 + 41x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-286 + 41x + -4x2)' equal to zero and attempt to solve:

Simplifying
-286 + 41x + -4x2 = 0

Solving
-286 + 41x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
71.5 + -10.25x + x2 = 0

Move the constant term to the right:

Add '-71.5' to each side of the equation.
71.5 + -10.25x + -71.5 + x2 = 0 + -71.5

Reorder the terms:
71.5 + -71.5 + -10.25x + x2 = 0 + -71.5

Combine like terms: 71.5 + -71.5 = 0.0
0.0 + -10.25x + x2 = 0 + -71.5
-10.25x + x2 = 0 + -71.5

Combine like terms: 0 + -71.5 = -71.5
-10.25x + x2 = -71.5

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = -71.5 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = -71.5 + 26.265625

Combine like terms: -71.5 + 26.265625 = -45.234375
26.265625 + -10.25x + x2 = -45.234375

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = -45.234375

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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