(x+3y)(4x-10y)=

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Solution for (x+3y)(4x-10y)= equation: 


Simplifying
(x + 3y)(4x + -10y) = 0

Multiply (x + 3y) * (4x + -10y)
(x(4x + -10y) + 3y * (4x + -10y)) = 0
((4x * x + -10y * x) + 3y * (4x + -10y)) = 0

Reorder the terms:
((-10xy + 4x2) + 3y * (4x + -10y)) = 0
((-10xy + 4x2) + 3y * (4x + -10y)) = 0
(-10xy + 4x2 + (4x * 3y + -10y * 3y)) = 0
(-10xy + 4x2 + (12xy + -30y2)) = 0

Reorder the terms:
(-10xy + 12xy + 4x2 + -30y2) = 0

Combine like terms: -10xy + 12xy = 2xy
(2xy + 4x2 + -30y2) = 0

Solving
2xy + 4x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + 2x2 + -15y2) = 0

Factor a trinomial.
2((2x + -5y)(x + 3y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {2.5y, -3y}

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