90=6P(P+10)

Simple and best practice solution for 90=6P(P+10) 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 90=6P(P+10) equation: 


Simplifying
90 = 6P(P + 10)

Reorder the terms:
90 = 6P(10 + P)
90 = (10 * 6P + P * 6P)
90 = (60P + 6P2)

Solving
90 = 60P + 6P2

Solving for variable 'P'.

Reorder the terms:
90 + -60P + -6P2 = 60P + -60P + 6P2 + -6P2

Combine like terms: 60P + -60P = 0
90 + -60P + -6P2 = 0 + 6P2 + -6P2
90 + -60P + -6P2 = 6P2 + -6P2

Combine like terms: 6P2 + -6P2 = 0
90 + -60P + -6P2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + -10P + -1P2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(15 + -10P + -1P2)' equal to zero and attempt to solve:

Simplifying
15 + -10P + -1P2 = 0

Solving
15 + -10P + -1P2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15 + 10P + P2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 10P + 15 + P2 = 0 + 15

Reorder the terms:
-15 + 15 + 10P + P2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 10P + P2 = 0 + 15
10P + P2 = 0 + 15

Combine like terms: 0 + 15 = 15
10P + P2 = 15

The P term is 10P.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10P + 25 + P2 = 15 + 25

Reorder the terms:
25 + 10P + P2 = 15 + 25

Combine like terms: 15 + 25 = 40
25 + 10P + P2 = 40

Factor a perfect square on the left side:
(P + 5)(P + 5) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(P + 5) equal to 6.32455532 and -6.32455532.


Subproblem 1
P + 5 = 6.32455532

Simplifying
P + 5 = 6.32455532

Reorder the terms:
5 + P = 6.32455532

Solving
5 + P = 6.32455532

Solving for variable 'P'.

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

Add '-5' to each side of the equation.
5 + -5 + P = 6.32455532 + -5

Combine like terms: 5 + -5 = 0
0 + P = 6.32455532 + -5
P = 6.32455532 + -5

Combine like terms: 6.32455532 + -5 = 1.32455532
P = 1.32455532

Simplifying
P = 1.32455532


Subproblem 2
P + 5 = -6.32455532

Simplifying
P + 5 = -6.32455532

Reorder the terms:
5 + P = -6.32455532

Solving
5 + P = -6.32455532

Solving for variable 'P'.

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

Add '-5' to each side of the equation.
5 + -5 + P = -6.32455532 + -5

Combine like terms: 5 + -5 = 0
0 + P = -6.32455532 + -5
P = -6.32455532 + -5

Combine like terms: -6.32455532 + -5 = -11.32455532
P = -11.32455532

Simplifying
P = -11.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
P = {1.32455532, -11.32455532}
Solution
P = {1.32455532, -11.32455532}

See similar equations:

| x^3+8x+21=3 | | 41p-2=61p-62 | | x^3+8x+18=0 | | 28-8x=c | | 6-8m=6-8m | | (4z-10)=1 | | 9x-(8x+8)=2x-47 | | 39c+25-16c=48 | | 7y-11=-21+2y | | 8-7x=3x+38 | | 11a+17-17a=49 | | -5t+4-x-1= | | y=-3x^2-7x-9 | | 7d+8-d=32 | | x*7+5=10 | | 49b+26-45b=30 | | 21xy^4+7x^2y^2= | | 2(4x-30)=10(x-10) | | 57p-13p+61p-p=128 | | 2b-3+7=19 | | 3x+71+5x+15=180 | | 7x-18=4x-6 | | 1-7(2n+3)=36-7n | | 436(3f)+322f=6600 | | 5b-1=8b-10 | | 45q-34=52q-76 | | 35x-21= | | h+(-18)=15 | | -5-3b=4-6b | | 2(-1+x)=9 | | 4.36b+3.22f=66 | | 5x+15=155-2x |

Equations solver categories