(7x+2y)(x-10y)=0

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Solution for (7x+2y)(x-10y)=0 equation: 


Simplifying
(7x + 2y)(x + -10y) = 0

Multiply (7x + 2y) * (x + -10y)
(7x * (x + -10y) + 2y * (x + -10y)) = 0
((x * 7x + -10y * 7x) + 2y * (x + -10y)) = 0

Reorder the terms:
((-70xy + 7x2) + 2y * (x + -10y)) = 0
((-70xy + 7x2) + 2y * (x + -10y)) = 0
(-70xy + 7x2 + (x * 2y + -10y * 2y)) = 0
(-70xy + 7x2 + (2xy + -20y2)) = 0

Reorder the terms:
(-70xy + 2xy + 7x2 + -20y2) = 0

Combine like terms: -70xy + 2xy = -68xy
(-68xy + 7x2 + -20y2) = 0

Solving
-68xy + 7x2 + -20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -10y)(7x + 2y) = 0


Subproblem 1
Set the factor '(x + -10y)' equal to zero and attempt to solve:

Simplifying
x + -10y = 0

Solving
x + -10y = 0

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

Add '10y' to each side of the equation.
x + -10y + 10y = 0 + 10y

Combine like terms: -10y + 10y = 0
x + 0 = 0 + 10y
x = 0 + 10y
Remove the zero:
x = 10y

Simplifying
x = 10y

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

Simplifying
7x + 2y = 0

Solving
7x + 2y = 0

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

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

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

Divide each side by '7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y
Solution
x = {10y, -0.2857142857y}

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