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

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


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

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

Reorder the terms:
0 = 4((-20xy + 28x2) + 7y * (7x + -5y))
0 = 4((-20xy + 28x2) + 7y * (7x + -5y))
0 = 4(-20xy + 28x2 + (7x * 7y + -5y * 7y))
0 = 4(-20xy + 28x2 + (49xy + -35y2))

Reorder the terms:
0 = 4(-20xy + 49xy + 28x2 + -35y2)

Combine like terms: -20xy + 49xy = 29xy
0 = 4(29xy + 28x2 + -35y2)
0 = (29xy * 4 + 28x2 * 4 + -35y2 * 4)
0 = (116xy + 112x2 + -140y2)

Solving
0 = 116xy + 112x2 + -140y2

Solving for variable 'x'.
Remove the zero:
-116xy + -112x2 + 140y2 = 116xy + 112x2 + -140y2 + -116xy + -112x2 + 140y2

Reorder the terms:
-116xy + -112x2 + 140y2 = 116xy + -116xy + 112x2 + -112x2 + -140y2 + 140y2

Combine like terms: 116xy + -116xy = 0
-116xy + -112x2 + 140y2 = 0 + 112x2 + -112x2 + -140y2 + 140y2
-116xy + -112x2 + 140y2 = 112x2 + -112x2 + -140y2 + 140y2

Combine like terms: 112x2 + -112x2 = 0
-116xy + -112x2 + 140y2 = 0 + -140y2 + 140y2
-116xy + -112x2 + 140y2 = -140y2 + 140y2

Combine like terms: -140y2 + 140y2 = 0
-116xy + -112x2 + 140y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-29xy + -28x2 + 35y2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-4x + -7y)' equal to zero and attempt to solve:

Simplifying
-4x + -7y = 0

Solving
-4x + -7y = 0

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

Add '7y' to each side of the equation.
-4x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
-4x + 0 = 0 + 7y
-4x = 0 + 7y
Remove the zero:
-4x = 7y

Divide each side by '-4'.
x = -1.75y

Simplifying
x = -1.75y

Subproblem 2
Set the factor '(7x + -5y)' equal to zero and attempt to solve:

Simplifying
7x + -5y = 0

Solving
7x + -5y = 0

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

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

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

Divide each side by '7'.
x = 0.7142857143y

Simplifying
x = 0.7142857143y
Solution
x = {-1.75y, 0.7142857143y}

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