(x+11y)(4x+6y)=

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Solution for (x+11y)(4x+6y)= equation: 


Simplifying
(x + 11y)(4x + 6y) = 0

Multiply (x + 11y) * (4x + 6y)
(x(4x + 6y) + 11y * (4x + 6y)) = 0
((4x * x + 6y * x) + 11y * (4x + 6y)) = 0

Reorder the terms:
((6xy + 4x2) + 11y * (4x + 6y)) = 0
((6xy + 4x2) + 11y * (4x + 6y)) = 0
(6xy + 4x2 + (4x * 11y + 6y * 11y)) = 0
(6xy + 4x2 + (44xy + 66y2)) = 0

Reorder the terms:
(6xy + 44xy + 4x2 + 66y2) = 0

Combine like terms: 6xy + 44xy = 50xy
(50xy + 4x2 + 66y2) = 0

Solving
50xy + 4x2 + 66y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25xy + 2x2 + 33y2) = 0

Factor a trinomial.
2((2x + 3y)(x + 11y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

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

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

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 2
Set the factor '(x + 11y)' equal to zero and attempt to solve:

Simplifying
x + 11y = 0

Solving
x + 11y = 0

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

Add '-11y' to each side of the equation.
x + 11y + -11y = 0 + -11y

Combine like terms: 11y + -11y = 0
x + 0 = 0 + -11y
x = 0 + -11y
Remove the zero:
x = -11y

Simplifying
x = -11y
Solution
x = {-1.5y, -11y}

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