2x^2(x+2y)-2(7x^3-2x^2y)=

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Solution for 2x^2(x+2y)-2(7x^3-2x^2y)= equation: 


Simplifying
2x2(x + 2y) + -2(7x3 + -2x2y) = 0
(x * 2x2 + 2y * 2x2) + -2(7x3 + -2x2y) = 0

Reorder the terms:
(4x2y + 2x3) + -2(7x3 + -2x2y) = 0
(4x2y + 2x3) + -2(7x3 + -2x2y) = 0

Reorder the terms:
4x2y + 2x3 + -2(-2x2y + 7x3) = 0
4x2y + 2x3 + (-2x2y * -2 + 7x3 * -2) = 0
4x2y + 2x3 + (4x2y + -14x3) = 0

Reorder the terms:
4x2y + 4x2y + 2x3 + -14x3 = 0

Combine like terms: 4x2y + 4x2y = 8x2y
8x2y + 2x3 + -14x3 = 0

Combine like terms: 2x3 + -14x3 = -12x3
8x2y + -12x3 = 0

Solving
8x2y + -12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(2y + -3x) = 0

Ignore the factor 4.

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 '(2y + -3x)' equal to zero and attempt to solve:

Simplifying
2y + -3x = 0

Reorder the terms:
-3x + 2y = 0

Solving
-3x + 2y = 0

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

Add '-2y' to each side of the equation.
-3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-3x + 0 = 0 + -2y
-3x = 0 + -2y
Remove the zero:
-3x = -2y

Divide each side by '-3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {0, 0.6666666667y}

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