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

Simple and best practice solution for 4p+25=6p(p-3)-3(4-3p) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

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}

See similar equations:

| -3(m-2)=6(4m+1) | | -6-8=-2+x | | 6x-3x+4-2x= | | -14+3=m-10 | | u/4=8/3 | | 6j=3 | | (5/3x^2y)-(4/6xy^3) | | -3(x+9)-44=5-52 | | 2t-5t-7=11 | | (5/3^2y)-(4/6xy^2) | | 7t-17=-29+t | | 48=6(e^4k) | | 1.05x=12.59-x | | -16x^2y^7/12x^5y^3z^4 | | (4x)(-4x)=84 | | 5X+11=12X-3 | | 15(4-y)=5(10+2y) | | 3d+2k=44 | | 1.05x=12.59 | | 8s-23=-21+7s | | 4r^2-8r+4=0 | | 16=3y-11 | | 7x=4-(-17) | | .5x=12.59 | | 8x+4=9x+2 | | -5(8x+8)+1= | | 5/15=6/n | | 11a=44 | | 1/20=n/300 | | 10a^3b/-15ab^3 | | ln(7a)=0 | | 3*x+4=37 |

Equations solver categories