(p-3s)(-4p+6s)=

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Solution for (p-3s)(-4p+6s)= equation: 


Simplifying
(p + -3s)(-4p + 6s) = 0

Multiply (p + -3s) * (-4p + 6s)
(p(-4p + 6s) + -3s * (-4p + 6s)) = 0
((-4p * p + 6s * p) + -3s * (-4p + 6s)) = 0

Reorder the terms:
((6ps + -4p2) + -3s * (-4p + 6s)) = 0
((6ps + -4p2) + -3s * (-4p + 6s)) = 0
(6ps + -4p2 + (-4p * -3s + 6s * -3s)) = 0
(6ps + -4p2 + (12ps + -18s2)) = 0

Reorder the terms:
(6ps + 12ps + -4p2 + -18s2) = 0

Combine like terms: 6ps + 12ps = 18ps
(18ps + -4p2 + -18s2) = 0

Solving
18ps + -4p2 + -18s2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9ps + -2p2 + -9s2) = 0

Factor a trinomial.
2((-2p + 3s)(p + -3s)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2p + 3s)' equal to zero and attempt to solve:

Simplifying
-2p + 3s = 0

Solving
-2p + 3s = 0

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

Add '-3s' to each side of the equation.
-2p + 3s + -3s = 0 + -3s

Combine like terms: 3s + -3s = 0
-2p + 0 = 0 + -3s
-2p = 0 + -3s
Remove the zero:
-2p = -3s

Divide each side by '-2'.
p = 1.5s

Simplifying
p = 1.5s

Subproblem 2
Set the factor '(p + -3s)' equal to zero and attempt to solve:

Simplifying
p + -3s = 0

Solving
p + -3s = 0

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

Add '3s' to each side of the equation.
p + -3s + 3s = 0 + 3s

Combine like terms: -3s + 3s = 0
p + 0 = 0 + 3s
p = 0 + 3s
Remove the zero:
p = 3s

Simplifying
p = 3s
Solution
p = {1.5s, 3s}

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