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

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


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

Reorder the terms for easier multiplication:
x(5x + 7y)(3x + -4y) = 0

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

Reorder the terms:
x((-20xy + 15x2) + 7y * (3x + -4y)) = 0
x((-20xy + 15x2) + 7y * (3x + -4y)) = 0
x(-20xy + 15x2 + (3x * 7y + -4y * 7y)) = 0
x(-20xy + 15x2 + (21xy + -28y2)) = 0

Reorder the terms:
x(-20xy + 21xy + 15x2 + -28y2) = 0

Combine like terms: -20xy + 21xy = 1xy
x(1xy + 15x2 + -28y2) = 0
(1xy * x + 15x2 * x + -28y2 * x) = 0

Reorder the terms:
(-28xy2 + 1x2y + 15x3) = 0
(-28xy2 + 1x2y + 15x3) = 0

Solving
-28xy2 + 1x2y + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-28y2 + xy + 15x2) = 0

Factor a trinomial.
x((-7y + -5x)(4y + -3x)) = 0


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 + -5x)' equal to zero and attempt to solve:

Simplifying
-7y + -5x = 0

Reorder the terms:
-5x + -7y = 0

Solving
-5x + -7y = 0

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

Add '7y' to each side of the equation.
-5x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
-5x + 0 = 0 + 7y
-5x = 0 + 7y
Remove the zero:
-5x = 7y

Divide each side by '-5'.
x = -1.4y

Simplifying
x = -1.4y

Subproblem 3
Set the factor '(4y + -3x)' equal to zero and attempt to solve:

Simplifying
4y + -3x = 0

Reorder the terms:
-3x + 4y = 0

Solving
-3x + 4y = 0

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

Add '-4y' to each side of the equation.
-3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
-3x + 0 = 0 + -4y
-3x = 0 + -4y
Remove the zero:
-3x = -4y

Divide each side by '-3'.
x = 1.333333333y

Simplifying
x = 1.333333333y
Solution
x = {0, -1.4y, 1.333333333y}

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