(-36x^2+144x-60)=0

Simple and best practice solution for (-36x^2+144x-60)=0 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 (-36x^2+144x-60)=0 equation: 


Simplifying
(-36x2 + 144x + -60) = 0

Reorder the terms:
(-60 + 144x + -36x2) = 0

Remove parenthesis around (-60 + 144x + -36x2)
-60 + 144x + -36x2 = 0

Solving
-60 + 144x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-5 + 12x + -3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-5 + 12x + -3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + -3x2 = 0

Solving
-5 + 12x + -3x2 = 0

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

Divide each side by '-3'.
1.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -4x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -4x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + -1.666666667
-4x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-4x + x2 = -1.666666667

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

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.666666667 + 4

Reorder the terms:
4 + -4x + x2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + -4x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -2) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + -2 = 1.527525232

Simplifying
x + -2 = 1.527525232

Reorder the terms:
-2 + x = 1.527525232

Solving
-2 + x = 1.527525232

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.527525232 + 2
x = 1.527525232 + 2

Combine like terms: 1.527525232 + 2 = 3.527525232
x = 3.527525232

Simplifying
x = 3.527525232


Subproblem 2
x + -2 = -1.527525232

Simplifying
x + -2 = -1.527525232

Reorder the terms:
-2 + x = -1.527525232

Solving
-2 + x = -1.527525232

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.527525232 + 2
x = -1.527525232 + 2

Combine like terms: -1.527525232 + 2 = 0.472474768
x = 0.472474768

Simplifying
x = 0.472474768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.527525232, 0.472474768}
Solution
x = {3.527525232, 0.472474768}

See similar equations:

| 11-2(8+30)=49 | | -7(x+1)-12=41+3 | | 84y^2+y-9=0 | | 3.6-2.4d=24 | | 8(x+3)+5(x+3)=7x-7 | | 9x+12y=3 | | X+15=3x+20 | | -7(x+1)-12=14+3 | | 1-x^5=0 | | 5a+9c=a | | 8(x+3)+5(x+3)=7x-3 | | 10(x+1)+4x+14+22=82 | | 4x+8+2x+3=180 | | 4x+62+2x+28=180 | | 6x+87+3x+57=180 | | 6x-x+x=18 | | -81+9w=36 | | .7(x+100)+.7x=119 | | 12-4w=-12 | | 19-g=11 | | a=2(2.8(3.5)+7.1(3.5)+2.8(3.5)) | | 12+3(a+2b)-2a-3b-9+b= | | 6x+8-2x+10=46 | | 17n-(-10)n=-18n-63 | | 3x+15*4x-12=y | | (0.3)(0.7)= | | 4x-96=5x+12 | | 0=x^2+4x+8 | | 8x+3=9x-20 | | 4.5(2.2)-3.5t=19 | | 17-6n=47-10n | | 4x-27=69 |

Equations solver categories