p(4p+12)=144

Simple and best practice solution for p(4p+12)=144 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 p(4p+12)=144 equation: 


Simplifying
p(4p + 12) = 144

Reorder the terms:
p(12 + 4p) = 144
(12 * p + 4p * p) = 144
(12p + 4p2) = 144

Solving
12p + 4p2 = 144

Solving for variable 'p'.

Reorder the terms:
-144 + 12p + 4p2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + 12p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 3p + p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-36 + 3p + p2)' equal to zero and attempt to solve:

Simplifying
-36 + 3p + p2 = 0

Solving
-36 + 3p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 3p + 36 + p2 = 0 + 36

Reorder the terms:
-36 + 36 + 3p + p2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 3p + p2 = 0 + 36
3p + p2 = 0 + 36

Combine like terms: 0 + 36 = 36
3p + p2 = 36

The p term is 3p.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3p + 2.25 + p2 = 36 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + 3p + p2 = 38.25

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(p + 1.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
p + 1.5 = 6.184658438

Simplifying
p + 1.5 = 6.184658438

Reorder the terms:
1.5 + p = 6.184658438

Solving
1.5 + p = 6.184658438

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = 6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = 6.184658438 + -1.5
p = 6.184658438 + -1.5

Combine like terms: 6.184658438 + -1.5 = 4.684658438
p = 4.684658438

Simplifying
p = 4.684658438


Subproblem 2
p + 1.5 = -6.184658438

Simplifying
p + 1.5 = -6.184658438

Reorder the terms:
1.5 + p = -6.184658438

Solving
1.5 + p = -6.184658438

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = -6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = -6.184658438 + -1.5
p = -6.184658438 + -1.5

Combine like terms: -6.184658438 + -1.5 = -7.684658438
p = -7.684658438

Simplifying
p = -7.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.684658438, -7.684658438}
Solution
p = {4.684658438, -7.684658438}

See similar equations:

| p(p+16)=0 | | 23-x=[6-(6-7)]-(4-6)3 | | 2x+4=16+72*8 | | 2x+35.75=x^2 | | 3k-15=27 | | 8x+143-4x^2=0 | | ln(Cos(180^2)/2)) | | 8x-41+9x+17=10 | | ln(cos(180^2/2)) | | 5/7-2x0 | | 5/7-2x | | -3(t-1)+6t=5t-5 | | 7x-51+2x=3-7x+10 | | -3y+3=3(2y+7) | | 9x^2-42x-45=0 | | F(x)=-10x+4 | | 6z^2-20z+16= | | 5v^2+4v+4=0 | | m^2=19m-90 | | (2x-1)-(2x^2)= | | 5x-(x-4)=9 | | (6/25)=(x/21) | | 6/25=x/21 | | 32+(x+1)2=(x+2)2 | | ln(2x+1)=-3 | | 7/5(x-22) | | 2y^2+y=28 | | 3p-2(2p-5)=2(p+3)-8 | | Y-k=k(x+y) | | X^2-64x-11520=0 | | Wsquared+4w-168=0 | | 3(2+X)=3x+4 |

Equations solver categories