2x(2x-3y+4)-8x(y+1)=

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Solution for 2x(2x-3y+4)-8x(y+1)= equation: 


Simplifying
2x(2x + -3y + 4) + -8x(y + 1) = 0

Reorder the terms:
2x(4 + 2x + -3y) + -8x(y + 1) = 0
(4 * 2x + 2x * 2x + -3y * 2x) + -8x(y + 1) = 0

Reorder the terms:
(8x + -6xy + 4x2) + -8x(y + 1) = 0
(8x + -6xy + 4x2) + -8x(y + 1) = 0

Reorder the terms:
8x + -6xy + 4x2 + -8x(1 + y) = 0
8x + -6xy + 4x2 + (1 * -8x + y * -8x) = 0
8x + -6xy + 4x2 + (-8x + -8xy) = 0

Reorder the terms:
8x + -8x + -6xy + -8xy + 4x2 = 0

Combine like terms: 8x + -8x = 0
0 + -6xy + -8xy + 4x2 = 0
-6xy + -8xy + 4x2 = 0

Combine like terms: -6xy + -8xy = -14xy
-14xy + 4x2 = 0

Solving
-14xy + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-7y + 2x) = 0

Ignore the factor 2.

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 '(-7y + 2x)' equal to zero and attempt to solve:

Simplifying
-7y + 2x = 0

Reorder the terms:
2x + -7y = 0

Solving
2x + -7y = 0

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

Add '7y' to each side of the equation.
2x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
2x + 0 = 0 + 7y
2x = 0 + 7y
Remove the zero:
2x = 7y

Divide each side by '2'.
x = 3.5y

Simplifying
x = 3.5y
Solution
x = {0, 3.5y}

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