4p+25=6p(p-3)-3(4-3p)

Solution for 4p+25=6p(p-3)-3(4-3p) equation:

Simplifying
4p + 25 = 6p(p + -3) + -3(4 + -3p)

Reorder the terms:
25 + 4p = 6p(p + -3) + -3(4 + -3p)

Reorder the terms:
25 + 4p = 6p(-3 + p) + -3(4 + -3p)
25 + 4p = (-3 * 6p + p * 6p) + -3(4 + -3p)
25 + 4p = (-18p + 6p2) + -3(4 + -3p)
25 + 4p = -18p + 6p2 + (4 * -3 + -3p * -3)
25 + 4p = -18p + 6p2 + (-12 + 9p)

Reorder the terms:
25 + 4p = -12 + -18p + 9p + 6p2

Combine like terms: -18p + 9p = -9p
25 + 4p = -12 + -9p + 6p2

Solving
25 + 4p = -12 + -9p + 6p2

Solving for variable 'p'.

Reorder the terms:
25 + 12 + 4p + 9p + -6p2 = -12 + -9p + 6p2 + 12 + 9p + -6p2

Combine like terms: 25 + 12 = 37
37 + 4p + 9p + -6p2 = -12 + -9p + 6p2 + 12 + 9p + -6p2

Combine like terms: 4p + 9p = 13p
37 + 13p + -6p2 = -12 + -9p + 6p2 + 12 + 9p + -6p2

Reorder the terms:
37 + 13p + -6p2 = -12 + 12 + -9p + 9p + 6p2 + -6p2

Combine like terms: -12 + 12 = 0
37 + 13p + -6p2 = 0 + -9p + 9p + 6p2 + -6p2
37 + 13p + -6p2 = -9p + 9p + 6p2 + -6p2

Combine like terms: -9p + 9p = 0
37 + 13p + -6p2 = 0 + 6p2 + -6p2
37 + 13p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
37 + 13p + -6p2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-6.166666667 + -2.166666667p + p2 = 0

Move the constant term to the right:

Add '6.166666667' to each side of the equation.
-6.166666667 + -2.166666667p + 6.166666667 + p2 = 0 + 6.166666667

Reorder the terms:
-6.166666667 + 6.166666667 + -2.166666667p + p2 = 0 + 6.166666667

Combine like terms: -6.166666667 + 6.166666667 = 0.000000000
0.000000000 + -2.166666667p + p2 = 0 + 6.166666667
-2.166666667p + p2 = 0 + 6.166666667

Combine like terms: 0 + 6.166666667 = 6.166666667
-2.166666667p + p2 = 6.166666667

The p term is -2.166666667p.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667p + 1.173611113 + p2 = 6.166666667 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667p + p2 = 6.166666667 + 1.173611113

Combine like terms: 6.166666667 + 1.173611113 = 7.34027778
1.173611113 + -2.166666667p + p2 = 7.34027778

Factor a perfect square on the left side:
(p + -1.083333334)(p + -1.083333334) = 7.34027778

Calculate the square root of the right side: 2.709294702

Break this problem into two subproblems by setting 
(p + -1.083333334) equal to 2.709294702 and -2.709294702.

Subproblem 1
p + -1.083333334 = 2.709294702

Simplifying
p + -1.083333334 = 2.709294702

Reorder the terms:
-1.083333334 + p = 2.709294702

Solving
-1.083333334 + p = 2.709294702

Solving for variable 'p'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + p = 2.709294702 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + p = 2.709294702 + 1.083333334
p = 2.709294702 + 1.083333334

Combine like terms: 2.709294702 + 1.083333334 = 3.792628036
p = 3.792628036

Simplifying
p = 3.792628036

Subproblem 2
p + -1.083333334 = -2.709294702

Simplifying
p + -1.083333334 = -2.709294702

Reorder the terms:
-1.083333334 + p = -2.709294702

Solving
-1.083333334 + p = -2.709294702

Solving for variable 'p'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + p = -2.709294702 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + p = -2.709294702 + 1.083333334
p = -2.709294702 + 1.083333334

Combine like terms: -2.709294702 + 1.083333334 = -1.625961368
p = -1.625961368

Simplifying
p = -1.625961368

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.792628036, -1.625961368}