7x^2(x-4y+6)-4x^2y=

Solution for 7x^2(x-4y+6)-4x^2y= equation:

Simplifying
7x2(x + -4y + 6) + -4x2y = 0

Reorder the terms:
7x2(6 + x + -4y) + -4x2y = 0
(6 * 7x2 + x * 7x2 + -4y * 7x2) + -4x2y = 0

Reorder the terms:
(42x2 + -28x2y + 7x3) + -4x2y = 0
(42x2 + -28x2y + 7x3) + -4x2y = 0

Reorder the terms:
42x2 + -28x2y + -4x2y + 7x3 = 0

Combine like terms: -28x2y + -4x2y = -32x2y
42x2 + -32x2y + 7x3 = 0

Solving
42x2 + -32x2y + 7x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(42 + -32y + 7x) = 0

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 '(42 + -32y + 7x)' equal to zero and attempt to solve:

Simplifying
42 + -32y + 7x = 0

Reorder the terms:
42 + 7x + -32y = 0

Solving
42 + 7x + -32y = 0

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

Add '-42' to each side of the equation.
42 + 7x + -42 + -32y = 0 + -42

Reorder the terms:
42 + -42 + 7x + -32y = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 7x + -32y = 0 + -42
7x + -32y = 0 + -42

Combine like terms: 0 + -42 = -42
7x + -32y = -42

Add '32y' to each side of the equation.
7x + -32y + 32y = -42 + 32y

Combine like terms: -32y + 32y = 0
7x + 0 = -42 + 32y
7x = -42 + 32y

Divide each side by '7'.
x = -6 + 4.571428571y

Simplifying
x = -6 + 4.571428571y
Solution
x = {0, -6 + 4.571428571y}