3r^2-12r+4=10

Simple and best practice solution for 3r^2-12r+4=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 3r^2-12r+4=10 equation: 


Simplifying
3r2 + -12r + 4 = 10

Reorder the terms:
4 + -12r + 3r2 = 10

Solving
4 + -12r + 3r2 = 10

Solving for variable 'r'.

Reorder the terms:
4 + -10 + -12r + 3r2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + -12r + 3r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + -12r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -4r + r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -4r + r2)' equal to zero and attempt to solve:

Simplifying
-2 + -4r + r2 = 0

Solving
-2 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -4r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4r + r2 = 0 + 2
-4r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4r + r2 = 2

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 2 + 4

Reorder the terms:
4 + -4r + r2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4r + r2 = 6

Factor a perfect square on the left side:
(r + -2)(r + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(r + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
r + -2 = 2.449489743

Simplifying
r + -2 = 2.449489743

Reorder the terms:
-2 + r = 2.449489743

Solving
-2 + r = 2.449489743

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + r = 2.449489743 + 2
r = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
r = 4.449489743

Simplifying
r = 4.449489743


Subproblem 2
r + -2 = -2.449489743

Simplifying
r + -2 = -2.449489743

Reorder the terms:
-2 + r = -2.449489743

Solving
-2 + r = -2.449489743

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + r = -2.449489743 + 2
r = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
r = -0.449489743

Simplifying
r = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.449489743, -0.449489743}
Solution
r = {4.449489743, -0.449489743}

See similar equations:

| (2x^2-1)-24=0 | | -47-12x=85-6x | | 11.3n+5.6=28.2 | | (x+8)(6x-7)=0 | | 2x-5=5x+27 | | 5x-18=-83 | | x=364*455*195 | | -113+3x=76+10x | | g=3*4 | | 17.88*5= | | 25*x-19=56 | | 6x+8=7x-6 | | x-3=-14.2 | | 2(x-3)-3(x-1)=0 | | 5x=2(3x+11) | | (-x)(3x)= | | 6b^2+b-70=0 | | 5x-6+3x=26 | | 30x^2+5x-25=0 | | 5w+6-12w=-29 | | m^2+2m-48=0 | | 6=8x+x | | x^2+10x+41=0 | | 7(-3z)+3=-6(z-4)-8 | | (6m-11)(3m+7)=0 | | 12x-20=8x | | 3d-2=12 | | 8t+5-7t=22 | | g^2+3g-54=0 | | -x-9=11,2 | | 3a+2+4a=24 | | 1-y=0 |

Equations solver categories