3p(p-10)-6(5-3p)=

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Solution for 3p(p-10)-6(5-3p)= equation: 


Simplifying
3p(p + -10) + -6(5 + -3p) = 0

Reorder the terms:
3p(-10 + p) + -6(5 + -3p) = 0
(-10 * 3p + p * 3p) + -6(5 + -3p) = 0
(-30p + 3p2) + -6(5 + -3p) = 0
-30p + 3p2 + (5 * -6 + -3p * -6) = 0
-30p + 3p2 + (-30 + 18p) = 0

Reorder the terms:
-30 + -30p + 18p + 3p2 = 0

Combine like terms: -30p + 18p = -12p
-30 + -12p + 3p2 = 0

Solving
-30 + -12p + 3p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -4p + p2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + -4p + p2)' equal to zero and attempt to solve:

Simplifying
-10 + -4p + p2 = 0

Solving
-10 + -4p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -4p + 10 + p2 = 0 + 10

Reorder the terms:
-10 + 10 + -4p + p2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -4p + p2 = 0 + 10
-4p + p2 = 0 + 10

Combine like terms: 0 + 10 = 10
-4p + p2 = 10

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 10 + 4

Reorder the terms:
4 + -4p + p2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + -4p + p2 = 14

Factor a perfect square on the left side:
(p + -2)(p + -2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(p + -2) equal to 3.741657387 and -3.741657387.


Subproblem 1
p + -2 = 3.741657387

Simplifying
p + -2 = 3.741657387

Reorder the terms:
-2 + p = 3.741657387

Solving
-2 + p = 3.741657387

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = 3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + p = 3.741657387 + 2
p = 3.741657387 + 2

Combine like terms: 3.741657387 + 2 = 5.741657387
p = 5.741657387

Simplifying
p = 5.741657387


Subproblem 2
p + -2 = -3.741657387

Simplifying
p + -2 = -3.741657387

Reorder the terms:
-2 + p = -3.741657387

Solving
-2 + p = -3.741657387

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = -3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + p = -3.741657387 + 2
p = -3.741657387 + 2

Combine like terms: -3.741657387 + 2 = -1.741657387
p = -1.741657387

Simplifying
p = -1.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.741657387, -1.741657387}
Solution
p = {5.741657387, -1.741657387}

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