6x^2(x^2+3xy-4y^2)=

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Solution for 6x^2(x^2+3xy-4y^2)= equation: 


Simplifying
6x2(x2 + 3xy + -4y2) = 0

Reorder the terms:
6x2(3xy + x2 + -4y2) = 0
(3xy * 6x2 + x2 * 6x2 + -4y2 * 6x2) = 0

Reorder the terms:
(-24x2y2 + 18x3y + 6x4) = 0
(-24x2y2 + 18x3y + 6x4) = 0

Solving
-24x2y2 + 18x3y + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-4y2 + 3xy + x2) = 0

Factor a trinomial.
6x2((-4y + -1x)(y + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
-4y + -1x = 0

Reorder the terms:
-1x + -4y = 0

Solving
-1x + -4y = 0

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

Add '4y' to each side of the equation.
-1x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
-1x + 0 = 0 + 4y
-1x = 0 + 4y
Remove the zero:
-1x = 4y

Divide each side by '-1'.
x = -4y

Simplifying
x = -4y

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

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

Add '-1y' to each side of the equation.
-1x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1x + 0 = 0 + -1y
-1x = 0 + -1y
Remove the zero:
-1x = -1y

Divide each side by '-1'.
x = y

Simplifying
x = y
Solution
x = {0, -4y, y}

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