6p(x-p)=2p(x+p)

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Solution for 6p(x-p)=2p(x+p) equation: 


Simplifying
6p(x + -1p) = 2p(x + p)

Reorder the terms:
6p(-1p + x) = 2p(x + p)
(-1p * 6p + x * 6p) = 2p(x + p)

Reorder the terms:
(6px + -6p2) = 2p(x + p)
(6px + -6p2) = 2p(x + p)

Reorder the terms:
6px + -6p2 = 2p(p + x)
6px + -6p2 = (p * 2p + x * 2p)

Reorder the terms:
6px + -6p2 = (2px + 2p2)
6px + -6p2 = (2px + 2p2)

Solving
6px + -6p2 = 2px + 2p2

Solving for variable 'p'.

Reorder the terms:
6px + -2px + -6p2 + -2p2 = 2px + 2p2 + -2px + -2p2

Combine like terms: 6px + -2px = 4px
4px + -6p2 + -2p2 = 2px + 2p2 + -2px + -2p2

Combine like terms: -6p2 + -2p2 = -8p2
4px + -8p2 = 2px + 2p2 + -2px + -2p2

Reorder the terms:
4px + -8p2 = 2px + -2px + 2p2 + -2p2

Combine like terms: 2px + -2px = 0
4px + -8p2 = 0 + 2p2 + -2p2
4px + -8p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
4px + -8p2 = 0

Factor out the Greatest Common Factor (GCF), '4p'.
4p(x + -2p) = 0

Ignore the factor 4.

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

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

Simplifying
x + -2p = 0

Reorder the terms:
-2p + x = 0

Solving
-2p + x = 0

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

Add '-1x' to each side of the equation.
-2p + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-2p + 0 = 0 + -1x
-2p = 0 + -1x
Remove the zero:
-2p = -1x

Divide each side by '-2'.
p = 0.5x

Simplifying
p = 0.5x
Solution
p = {0, 0.5x}

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