(6y^2+x)(y^2-7x)=0

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Solution for (6y^2+x)(y^2-7x)=0 equation: 


Simplifying
(6y2 + x)(y2 + -7x) = 0

Reorder the terms:
(x + 6y2)(y2 + -7x) = 0

Reorder the terms:
(x + 6y2)(-7x + y2) = 0

Multiply (x + 6y2) * (-7x + y2)
(x(-7x + y2) + 6y2 * (-7x + y2)) = 0
((-7x * x + y2 * x) + 6y2 * (-7x + y2)) = 0

Reorder the terms:
((xy2 + -7x2) + 6y2 * (-7x + y2)) = 0
((xy2 + -7x2) + 6y2 * (-7x + y2)) = 0
(xy2 + -7x2 + (-7x * 6y2 + y2 * 6y2)) = 0
(xy2 + -7x2 + (-42xy2 + 6y4)) = 0

Reorder the terms:
(xy2 + -42xy2 + -7x2 + 6y4) = 0

Combine like terms: xy2 + -42xy2 = -41xy2
(-41xy2 + -7x2 + 6y4) = 0

Solving
-41xy2 + -7x2 + 6y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -6y2)(7x + -1y2) = 0


Subproblem 1
Set the factor '(-1x + -6y2)' equal to zero and attempt to solve:

Simplifying
-1x + -6y2 = 0

Solving
-1x + -6y2 = 0

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

Add '6y2' to each side of the equation.
-1x + -6y2 + 6y2 = 0 + 6y2

Combine like terms: -6y2 + 6y2 = 0
-1x + 0 = 0 + 6y2
-1x = 0 + 6y2
Remove the zero:
-1x = 6y2

Divide each side by '-1'.
x = -6y2

Simplifying
x = -6y2

Subproblem 2
Set the factor '(7x + -1y2)' equal to zero and attempt to solve:

Simplifying
7x + -1y2 = 0

Solving
7x + -1y2 = 0

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

Add 'y2' to each side of the equation.
7x + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
7x + 0 = 0 + y2
7x = 0 + y2
Remove the zero:
7x = y2

Divide each side by '7'.
x = 0.1428571429y2

Simplifying
x = 0.1428571429y2
Solution
x = {-6y2, 0.1428571429y2}

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