2p+3p(p+3)=21

Simple and best practice solution for 2p+3p(p+3)=21 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 2p+3p(p+3)=21 equation:


Simplifying
2p + 3p(p + 3) = 21

Reorder the terms:
2p + 3p(3 + p) = 21
2p + (3 * 3p + p * 3p) = 21
2p + (9p + 3p2) = 21

Combine like terms: 2p + 9p = 11p
11p + 3p2 = 21

Solving
11p + 3p2 = 21

Solving for variable 'p'.

Reorder the terms:
-21 + 11p + 3p2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 11p + 3p2 = 0

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

Divide each side by '3'.
-7 + 3.666666667p + p2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3.666666667p + 7 + p2 = 0 + 7

Reorder the terms:
-7 + 7 + 3.666666667p + p2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3.666666667p + p2 = 0 + 7
3.666666667p + p2 = 0 + 7

Combine like terms: 0 + 7 = 7
3.666666667p + p2 = 7

The p term is 3.666666667p.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667p + 3.361111114 + p2 = 7 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667p + p2 = 7 + 3.361111114

Combine like terms: 7 + 3.361111114 = 10.361111114
3.361111114 + 3.666666667p + p2 = 10.361111114

Factor a perfect square on the left side:
(p + 1.833333334)(p + 1.833333334) = 10.361111114

Calculate the square root of the right side: 3.218867986

Break this problem into two subproblems by setting 
(p + 1.833333334) equal to 3.218867986 and -3.218867986.

Subproblem 1

p + 1.833333334 = 3.218867986 Simplifying p + 1.833333334 = 3.218867986 Reorder the terms: 1.833333334 + p = 3.218867986 Solving 1.833333334 + p = 3.218867986 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + p = 3.218867986 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + p = 3.218867986 + -1.833333334 p = 3.218867986 + -1.833333334 Combine like terms: 3.218867986 + -1.833333334 = 1.385534652 p = 1.385534652 Simplifying p = 1.385534652

Subproblem 2

p + 1.833333334 = -3.218867986 Simplifying p + 1.833333334 = -3.218867986 Reorder the terms: 1.833333334 + p = -3.218867986 Solving 1.833333334 + p = -3.218867986 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + p = -3.218867986 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + p = -3.218867986 + -1.833333334 p = -3.218867986 + -1.833333334 Combine like terms: -3.218867986 + -1.833333334 = -5.05220132 p = -5.05220132 Simplifying p = -5.05220132

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.385534652, -5.05220132}

See similar equations:

| 12-4x=11x-18 | | 150/9.7=s/90 | | (4x+8)(2x-8)= | | 8(z+3)-z=5z-11 | | 150/9.7=s/60 | | 2x^3+6x^2-18x+3=0 | | -4m=-12.8 | | b/47=-2 | | 7(8)/5+2 | | 8+i/1-2i | | (4/3)x+2=6 | | 4d^2+16=0 | | x-4=06 | | 7+5n=2n+6 | | 22x-y=-4 | | 6=9 | | 11c+-10c+-1=7 | | (2/5)x+10=0 | | 9/25=s/300 | | 6p^2+192p=-172 | | 4=5/-14 | | 6p^2+192=-172 | | 24x=188 | | (3/2)x+1=13 | | 6r+4r=-20 | | -2d/3+3=11 | | 18+4x=34 | | 10x-(4)2+8= | | 5n^2=-15n+200 | | 18w+-17w+-1=16 | | -12=(-8z)+12 | | 1/2x^2+5=55 |

Equations solver categories