3x(x-5)-2(x-2)(x+2)=(x+4)(x+1)-16

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Solution for 3x(x-5)-2(x-2)(x+2)=(x+4)(x+1)-16 equation: 


Simplifying
3x(x + -5) + -2(x + -2)(x + 2) = (x + 4)(x + 1) + -16

Reorder the terms:
3x(-5 + x) + -2(x + -2)(x + 2) = (x + 4)(x + 1) + -16
(-5 * 3x + x * 3x) + -2(x + -2)(x + 2) = (x + 4)(x + 1) + -16
(-15x + 3x2) + -2(x + -2)(x + 2) = (x + 4)(x + 1) + -16

Reorder the terms:
-15x + 3x2 + -2(-2 + x)(x + 2) = (x + 4)(x + 1) + -16

Reorder the terms:
-15x + 3x2 + -2(-2 + x)(2 + x) = (x + 4)(x + 1) + -16

Multiply (-2 + x) * (2 + x)
-15x + 3x2 + -2(-2(2 + x) + x(2 + x)) = (x + 4)(x + 1) + -16
-15x + 3x2 + -2((2 * -2 + x * -2) + x(2 + x)) = (x + 4)(x + 1) + -16
-15x + 3x2 + -2((-4 + -2x) + x(2 + x)) = (x + 4)(x + 1) + -16
-15x + 3x2 + -2(-4 + -2x + (2 * x + x * x)) = (x + 4)(x + 1) + -16
-15x + 3x2 + -2(-4 + -2x + (2x + x2)) = (x + 4)(x + 1) + -16

Combine like terms: -2x + 2x = 0
-15x + 3x2 + -2(-4 + 0 + x2) = (x + 4)(x + 1) + -16
-15x + 3x2 + -2(-4 + x2) = (x + 4)(x + 1) + -16
-15x + 3x2 + (-4 * -2 + x2 * -2) = (x + 4)(x + 1) + -16
-15x + 3x2 + (8 + -2x2) = (x + 4)(x + 1) + -16

Reorder the terms:
8 + -15x + 3x2 + -2x2 = (x + 4)(x + 1) + -16

Combine like terms: 3x2 + -2x2 = 1x2
8 + -15x + 1x2 = (x + 4)(x + 1) + -16

Reorder the terms:
8 + -15x + 1x2 = (4 + x)(x + 1) + -16

Reorder the terms:
8 + -15x + 1x2 = (4 + x)(1 + x) + -16

Multiply (4 + x) * (1 + x)
8 + -15x + 1x2 = (4(1 + x) + x(1 + x)) + -16
8 + -15x + 1x2 = ((1 * 4 + x * 4) + x(1 + x)) + -16
8 + -15x + 1x2 = ((4 + 4x) + x(1 + x)) + -16
8 + -15x + 1x2 = (4 + 4x + (1 * x + x * x)) + -16
8 + -15x + 1x2 = (4 + 4x + (1x + x2)) + -16

Combine like terms: 4x + 1x = 5x
8 + -15x + 1x2 = (4 + 5x + x2) + -16

Reorder the terms:
8 + -15x + 1x2 = 4 + -16 + 5x + x2

Combine like terms: 4 + -16 = -12
8 + -15x + 1x2 = -12 + 5x + x2

Solving
8 + -15x + 1x2 = -12 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
8 + 12 + -15x + -5x + 1x2 + -1x2 = -12 + 5x + x2 + 12 + -5x + -1x2

Combine like terms: 8 + 12 = 20
20 + -15x + -5x + 1x2 + -1x2 = -12 + 5x + x2 + 12 + -5x + -1x2

Combine like terms: -15x + -5x = -20x
20 + -20x + 1x2 + -1x2 = -12 + 5x + x2 + 12 + -5x + -1x2

Combine like terms: 1x2 + -1x2 = 0
20 + -20x + 0 = -12 + 5x + x2 + 12 + -5x + -1x2
20 + -20x = -12 + 5x + x2 + 12 + -5x + -1x2

Reorder the terms:
20 + -20x = -12 + 12 + 5x + -5x + x2 + -1x2

Combine like terms: -12 + 12 = 0
20 + -20x = 0 + 5x + -5x + x2 + -1x2
20 + -20x = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
20 + -20x = 0 + x2 + -1x2
20 + -20x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -20x = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(1 + -1x) = 0

Ignore the factor 20.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {1}

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