2x(5x-20)=x(8x+48)

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Solution for 2x(5x-20)=x(8x+48) equation: 


Simplifying
2x(5x + -20) = x(8x + 48)

Reorder the terms:
2x(-20 + 5x) = x(8x + 48)
(-20 * 2x + 5x * 2x) = x(8x + 48)
(-40x + 10x2) = x(8x + 48)

Reorder the terms:
-40x + 10x2 = x(48 + 8x)
-40x + 10x2 = (48 * x + 8x * x)
-40x + 10x2 = (48x + 8x2)

Solving
-40x + 10x2 = 48x + 8x2

Solving for variable 'x'.

Reorder the terms:
-40x + -48x + 10x2 + -8x2 = 48x + 8x2 + -48x + -8x2

Combine like terms: -40x + -48x = -88x
-88x + 10x2 + -8x2 = 48x + 8x2 + -48x + -8x2

Combine like terms: 10x2 + -8x2 = 2x2
-88x + 2x2 = 48x + 8x2 + -48x + -8x2

Reorder the terms:
-88x + 2x2 = 48x + -48x + 8x2 + -8x2

Combine like terms: 48x + -48x = 0
-88x + 2x2 = 0 + 8x2 + -8x2
-88x + 2x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-88x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-44 + x) = 0

Ignore the factor 2.

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 '(-44 + x)' equal to zero and attempt to solve:

Simplifying
-44 + x = 0

Solving
-44 + x = 0

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

Add '44' to each side of the equation.
-44 + 44 + x = 0 + 44

Combine like terms: -44 + 44 = 0
0 + x = 0 + 44
x = 0 + 44

Combine like terms: 0 + 44 = 44
x = 44

Simplifying
x = 44
Solution
x = {0, 44}

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