4c(c+3)=84

Simple and best practice solution for 4c(c+3)=84 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 4c(c+3)=84 equation: 


Simplifying
4c(c + 3) = 84

Reorder the terms:
4c(3 + c) = 84
(3 * 4c + c * 4c) = 84
(12c + 4c2) = 84

Solving
12c + 4c2 = 84

Solving for variable 'c'.

Reorder the terms:
-84 + 12c + 4c2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 12c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 3c + c2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-21 + 3c + c2)' equal to zero and attempt to solve:

Simplifying
-21 + 3c + c2 = 0

Solving
-21 + 3c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 3c + 21 + c2 = 0 + 21

Reorder the terms:
-21 + 21 + 3c + c2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 3c + c2 = 0 + 21
3c + c2 = 0 + 21

Combine like terms: 0 + 21 = 21
3c + c2 = 21

The c term is 3c.  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.
3c + 2.25 + c2 = 21 + 2.25

Reorder the terms:
2.25 + 3c + c2 = 21 + 2.25

Combine like terms: 21 + 2.25 = 23.25
2.25 + 3c + c2 = 23.25

Factor a perfect square on the left side:
(c + 1.5)(c + 1.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(c + 1.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
c + 1.5 = 4.82182538

Simplifying
c + 1.5 = 4.82182538

Reorder the terms:
1.5 + c = 4.82182538

Solving
1.5 + c = 4.82182538

Solving for variable 'c'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + c = 4.82182538 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + c = 4.82182538 + -1.5
c = 4.82182538 + -1.5

Combine like terms: 4.82182538 + -1.5 = 3.32182538
c = 3.32182538

Simplifying
c = 3.32182538


Subproblem 2
c + 1.5 = -4.82182538

Simplifying
c + 1.5 = -4.82182538

Reorder the terms:
1.5 + c = -4.82182538

Solving
1.5 + c = -4.82182538

Solving for variable 'c'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + c = -4.82182538 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + c = -4.82182538 + -1.5
c = -4.82182538 + -1.5

Combine like terms: -4.82182538 + -1.5 = -6.32182538
c = -6.32182538

Simplifying
c = -6.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.32182538, -6.32182538}
Solution
c = {3.32182538, -6.32182538}

See similar equations:

| 121=(x+6)(20-4x) | | 4m-8=44 | | 2k+1=k+5 | | 1/5(10x-5)=1/4(10x-8) | | y^2-23y-28=0 | | -v^2+11v-28=0 | | 4+9x^2=40 | | -u^2+8u-12=0 | | 6n^2=8n+11 | | 3x^2+14x+144=0 | | A+3b+70=100 | | x^2+14x+144=0 | | 66000=3x^2+4x+2 | | 25s^4t^7/5s^3t^9 | | 8xy-6xy+2xy= | | 62=3y+17 | | 0=-2/((m-2)(m-4)) | | x+3x-24= | | 0=-2/(m-2)(m-4) | | 3y^2+2x-3=0 | | 36k^2=49 | | x-8x+15= | | 3x-10x=0 | | 27x^4-72x^2+8x+36=0 | | x+20x+36= | | -8-(x/2)=-10 | | y+112=805 | | 29n=986 | | x/5-8=1 | | 835=k+35 | | f/20=20 | | 1/4(2x-9)=5 |

Equations solver categories