10p-2(3p-6)=4(5p-6)10p

Solution for 10p-2(3p-6)=4(5p-6)10p equation:

Simplifying
10p + -2(3p + -6) = 4(5p + -6) * 10p

Reorder the terms:
10p + -2(-6 + 3p) = 4(5p + -6) * 10p
10p + (-6 * -2 + 3p * -2) = 4(5p + -6) * 10p
10p + (12 + -6p) = 4(5p + -6) * 10p

Reorder the terms:
12 + 10p + -6p = 4(5p + -6) * 10p

Combine like terms: 10p + -6p = 4p
12 + 4p = 4(5p + -6) * 10p

Reorder the terms:
12 + 4p = 4(-6 + 5p) * 10p

Reorder the terms for easier multiplication:
12 + 4p = 4 * 10p(-6 + 5p)

Multiply 4 * 10
12 + 4p = 40p(-6 + 5p)
12 + 4p = (-6 * 40p + 5p * 40p)
12 + 4p = (-240p + 200p2)

Solving
12 + 4p = -240p + 200p2

Solving for variable 'p'.

Combine like terms: 4p + 240p = 244p
12 + 244p + -200p2 = -240p + 200p2 + 240p + -200p2

Reorder the terms:
12 + 244p + -200p2 = -240p + 240p + 200p2 + -200p2

Combine like terms: -240p + 240p = 0
12 + 244p + -200p2 = 0 + 200p2 + -200p2
12 + 244p + -200p2 = 200p2 + -200p2

Combine like terms: 200p2 + -200p2 = 0
12 + 244p + -200p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 61p + -50p2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 61p + -50p2)' equal to zero and attempt to solve:

Simplifying
3 + 61p + -50p2 = 0

Solving
3 + 61p + -50p2 = 0

Begin completing the square.  Divide all terms by
-50 the coefficient of the squared term: 

Divide each side by '-50'.
-0.06 + -1.22p + p2 = 0.0

Move the constant term to the right:

Add '0.06' to each side of the equation.
-0.06 + -1.22p + 0.06 + p2 = 0.0 + 0.06

Reorder the terms:
-0.06 + 0.06 + -1.22p + p2 = 0.0 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + -1.22p + p2 = 0.0 + 0.06
-1.22p + p2 = 0.0 + 0.06

Combine like terms: 0.0 + 0.06 = 0.06
-1.22p + p2 = 0.06

The p term is -1.22p.  Take half its coefficient (-0.61).
Square it (0.3721) and add it to both sides.

Add '0.3721' to each side of the equation.
-1.22p + 0.3721 + p2 = 0.06 + 0.3721

Reorder the terms:
0.3721 + -1.22p + p2 = 0.06 + 0.3721

Combine like terms: 0.06 + 0.3721 = 0.4321
0.3721 + -1.22p + p2 = 0.4321

Factor a perfect square on the left side:
(p + -0.61)(p + -0.61) = 0.4321

Calculate the square root of the right side: 0.657343137

Break this problem into two subproblems by setting 
(p + -0.61) equal to 0.657343137 and -0.657343137.

Subproblem 1
p + -0.61 = 0.657343137

Simplifying
p + -0.61 = 0.657343137

Reorder the terms:
-0.61 + p = 0.657343137

Solving
-0.61 + p = 0.657343137

Solving for variable 'p'.

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

Add '0.61' to each side of the equation.
-0.61 + 0.61 + p = 0.657343137 + 0.61

Combine like terms: -0.61 + 0.61 = 0.00
0.00 + p = 0.657343137 + 0.61
p = 0.657343137 + 0.61

Combine like terms: 0.657343137 + 0.61 = 1.267343137
p = 1.267343137

Simplifying
p = 1.267343137

Subproblem 2
p + -0.61 = -0.657343137

Simplifying
p + -0.61 = -0.657343137

Reorder the terms:
-0.61 + p = -0.657343137

Solving
-0.61 + p = -0.657343137

Solving for variable 'p'.

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

Add '0.61' to each side of the equation.
-0.61 + 0.61 + p = -0.657343137 + 0.61

Combine like terms: -0.61 + 0.61 = 0.00
0.00 + p = -0.657343137 + 0.61
p = -0.657343137 + 0.61

Combine like terms: -0.657343137 + 0.61 = -0.047343137
p = -0.047343137

Simplifying
p = -0.047343137

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.267343137, -0.047343137}
Solution
p = {1.267343137, -0.047343137}