27a^3+18a^2-3a=0

Simple and best practice solution for 27a^3+18a^2-3a=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 27a^3+18a^2-3a=0 equation:


Simplifying
27a3 + 18a2 + -3a = 0

Reorder the terms:
-3a + 18a2 + 27a3 = 0

Solving
-3a + 18a2 + 27a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-1 + 6a + 9a2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(-1 + 6a + 9a2)' equal to zero and attempt to solve: Simplifying -1 + 6a + 9a2 = 0 Solving -1 + 6a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + 0.6666666667a + a2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.6666666667a + 0.1111111111 + a2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.6666666667a + a2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.6666666667a + a2 = 0 + 0.1111111111 0.6666666667a + a2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.6666666667a + a2 = 0.1111111111 The a term is 0.6666666667a. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667a + 0.1111111112 + a2 = 0.1111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667a + a2 = 0.1111111111 + 0.1111111112 Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223 0.1111111112 + 0.6666666667a + a2 = 0.2222222223 Factor a perfect square on the left side: (a + 0.3333333334)(a + 0.3333333334) = 0.2222222223 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (a + 0.3333333334) equal to 0.471404521 and -0.471404521.

Subproblem 1

a + 0.3333333334 = 0.471404521 Simplifying a + 0.3333333334 = 0.471404521 Reorder the terms: 0.3333333334 + a = 0.471404521 Solving 0.3333333334 + a = 0.471404521 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + a = 0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + a = 0.471404521 + -0.3333333334 a = 0.471404521 + -0.3333333334 Combine like terms: 0.471404521 + -0.3333333334 = 0.1380711876 a = 0.1380711876 Simplifying a = 0.1380711876

Subproblem 2

a + 0.3333333334 = -0.471404521 Simplifying a + 0.3333333334 = -0.471404521 Reorder the terms: 0.3333333334 + a = -0.471404521 Solving 0.3333333334 + a = -0.471404521 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + a = -0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + a = -0.471404521 + -0.3333333334 a = -0.471404521 + -0.3333333334 Combine like terms: -0.471404521 + -0.3333333334 = -0.8047378544 a = -0.8047378544 Simplifying a = -0.8047378544

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.1380711876, -0.8047378544}

Solution

a = {0, 0.1380711876, -0.8047378544}

See similar equations:

| q+5=3q | | 6(8+5)=-348 | | -8+x+4x=47 | | x+qy=r | | 99=6(u+3)+3 | | 3y-6-6y=9 | | .4x=5-.1x | | 13x=506y+1 | | 2w^2+18w+30= | | 4(5z-1)-5(z+4)=10(z+1) | | 2ab+b=0 | | 5x=48y+1 | | 5x^2+5x-100= | | 5(2r-3)=6(x-1)+4x | | 5(5y+8)+6y=9 | | 4w^2-36w+72= | | 2v^2+24v+70= | | 5u^2+30u-70= | | 3(x-5)=2(q+5) | | 5u^2+3u-70= | | 3x+4x-29=-72 | | 130=2((4x)+(5x+2)) | | X+9=4(2x-1) | | (9*7)*2=9*(7*2) | | 3X-6=5(X-8) | | -7(p+19)=-28 | | -30(-x+6)+(-5x+4)=-5x-6+(-8+30) | | -8x+4(1+5x)=-6x-13 | | 4u^2+12u-72= | | 10-0.5000x=0 | | 39=2n-1 | | -3x+19y=-29 |

Equations solver categories