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

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


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

Reorder the terms:
4x(-5 + x) + 16 = 16 + 5x(x + -2)
(-5 * 4x + x * 4x) + 16 = 16 + 5x(x + -2)
(-20x + 4x2) + 16 = 16 + 5x(x + -2)

Reorder the terms:
16 + -20x + 4x2 = 16 + 5x(x + -2)

Reorder the terms:
16 + -20x + 4x2 = 16 + 5x(-2 + x)
16 + -20x + 4x2 = 16 + (-2 * 5x + x * 5x)
16 + -20x + 4x2 = 16 + (-10x + 5x2)

Add '-16' to each side of the equation.
16 + -20x + -16 + 4x2 = 16 + -10x + -16 + 5x2

Reorder the terms:
16 + -16 + -20x + 4x2 = 16 + -10x + -16 + 5x2

Combine like terms: 16 + -16 = 0
0 + -20x + 4x2 = 16 + -10x + -16 + 5x2
-20x + 4x2 = 16 + -10x + -16 + 5x2

Reorder the terms:
-20x + 4x2 = 16 + -16 + -10x + 5x2

Combine like terms: 16 + -16 = 0
-20x + 4x2 = 0 + -10x + 5x2
-20x + 4x2 = -10x + 5x2

Solving
-20x + 4x2 = -10x + 5x2

Solving for variable 'x'.

Reorder the terms:
-20x + 10x + 4x2 + -5x2 = -10x + 5x2 + 10x + -5x2

Combine like terms: -20x + 10x = -10x
-10x + 4x2 + -5x2 = -10x + 5x2 + 10x + -5x2

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

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

Combine like terms: -10x + 10x = 0
-10x + -1x2 = 0 + 5x2 + -5x2
-10x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(10 + x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {0, -10}

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