(7x-4y)(x+2y)-5x(y-3x)=0

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Solution for (7x-4y)(x+2y)-5x(y-3x)=0 equation: 


Simplifying
(7x + -4y)(x + 2y) + -5x(y + -3x) = 0

Multiply (7x + -4y) * (x + 2y)
(7x * (x + 2y) + -4y * (x + 2y)) + -5x(y + -3x) = 0
((x * 7x + 2y * 7x) + -4y * (x + 2y)) + -5x(y + -3x) = 0

Reorder the terms:
((14xy + 7x2) + -4y * (x + 2y)) + -5x(y + -3x) = 0
((14xy + 7x2) + -4y * (x + 2y)) + -5x(y + -3x) = 0
(14xy + 7x2 + (x * -4y + 2y * -4y)) + -5x(y + -3x) = 0
(14xy + 7x2 + (-4xy + -8y2)) + -5x(y + -3x) = 0

Reorder the terms:
(14xy + -4xy + 7x2 + -8y2) + -5x(y + -3x) = 0

Combine like terms: 14xy + -4xy = 10xy
(10xy + 7x2 + -8y2) + -5x(y + -3x) = 0

Reorder the terms:
10xy + 7x2 + -8y2 + -5x(-3x + y) = 0
10xy + 7x2 + -8y2 + (-3x * -5x + y * -5x) = 0

Reorder the terms:
10xy + 7x2 + -8y2 + (-5xy + 15x2) = 0
10xy + 7x2 + -8y2 + (-5xy + 15x2) = 0

Reorder the terms:
10xy + -5xy + 7x2 + 15x2 + -8y2 = 0

Combine like terms: 10xy + -5xy = 5xy
5xy + 7x2 + 15x2 + -8y2 = 0

Combine like terms: 7x2 + 15x2 = 22x2
5xy + 22x2 + -8y2 = 0

Solving
5xy + 22x2 + -8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -1y)(11x + 8y) = 0


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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

Subproblem 2
Set the factor '(11x + 8y)' equal to zero and attempt to solve:

Simplifying
11x + 8y = 0

Solving
11x + 8y = 0

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

Add '-8y' to each side of the equation.
11x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
11x + 0 = 0 + -8y
11x = 0 + -8y
Remove the zero:
11x = -8y

Divide each side by '11'.
x = -0.7272727273y

Simplifying
x = -0.7272727273y
Solution
x = {0.5y, -0.7272727273y}

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