3x^3+6x^2-24x=ax(x+b)(x+c)

Simple and best practice solution for 3x^3+6x^2-24x=ax(x+b)(x+c) 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 3x^3+6x^2-24x=ax(x+b)(x+c) equation: 


Simplifying
3x3 + 6x2 + -24x = ax(x + b)(x + c)

Reorder the terms:
-24x + 6x2 + 3x3 = ax(x + b)(x + c)

Reorder the terms:
-24x + 6x2 + 3x3 = ax(b + x)(x + c)

Reorder the terms:
-24x + 6x2 + 3x3 = ax(b + x)(c + x)

Multiply (b + x) * (c + x)
-24x + 6x2 + 3x3 = ax(b(c + x) + x(c + x))
-24x + 6x2 + 3x3 = ax((c * b + x * b) + x(c + x))
-24x + 6x2 + 3x3 = ax((bc + bx) + x(c + x))
-24x + 6x2 + 3x3 = ax(bc + bx + (c * x + x * x))
-24x + 6x2 + 3x3 = ax(bc + bx + (cx + x2))
-24x + 6x2 + 3x3 = ax(bc + bx + cx + x2)
-24x + 6x2 + 3x3 = (bc * ax + bx * ax + cx * ax + x2 * ax)
-24x + 6x2 + 3x3 = (abcx + abx2 + acx2 + ax3)

Solving
-24x + 6x2 + 3x3 = abcx + abx2 + acx2 + ax3

Solving for variable 'x'.

Reorder the terms:
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = abcx + abx2 + acx2 + ax3 + -1abcx + -1abx2 + -1acx2 + -1ax3

Reorder the terms:
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = abcx + -1abcx + abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: abcx + -1abcx = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = 0 + abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: abx2 + -1abx2 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = 0 + acx2 + -1acx2 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: acx2 + -1acx2 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = 0 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = ax3 + -1ax3

Combine like terms: ax3 + -1ax3 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + 6x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1abc + -1abx + -1acx + -1ax2 + -24 + 6x + 3x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1abc + -1abx + -1acx + -1ax2 + -24 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1abc + -1abx + -1acx + -1ax2 + -24 + 6x + 3x2 = 0

Reorder the terms:
-24 + -1abc + -1abx + -1acx + -1ax2 + 6x + 3x2 = 0

Solving
-24 + -1abc + -1abx + -1acx + -1ax2 + 6x + 3x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

See similar equations:

| (7/8)/(7/6) | | 7/8÷7/6 | | 2x+3.4=718.6 | | 2x+8.3=723.7 | | (x^2)+(14x)+48=0 | | 9-7x-5x+2= | | Y-10/17=8/3 | | 2b^2+11b-6=0 | | 5m-6=-5+6m | | 6y-21=-39+9y | | Y-20y= | | 4(7x-1)-3(8x-2)= | | 5t+8t=5-3(t-5) | | (26-2x)*(21-2x)-300=0 | | (26-2x)*(21-2x)=0 | | e+9=12 | | a/3=43 | | 25mg=12.5 | | 0.7/10=n/100 | | 10x+4y-46=0 | | w^2+5W=682 | | w^2+5W=6 | | w^2+5W=6.82 | | 56-40x=70-36x | | 12-y=y-3 | | 3x-100=5-2x | | 15c^3+12c^2=0 | | 34+12x=50-4x | | 14-2x=20-3x | | X+5=19-x | | 5.5x-7=2.5x+2 | | 30=0.15x+x |

Equations solver categories