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

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


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

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

Reorder the terms:
((-20xz + 28x2) + 5z * (7x + -5z)) = 0
((-20xz + 28x2) + 5z * (7x + -5z)) = 0
(-20xz + 28x2 + (7x * 5z + -5z * 5z)) = 0
(-20xz + 28x2 + (35xz + -25z2)) = 0

Reorder the terms:
(-20xz + 35xz + 28x2 + -25z2) = 0

Combine like terms: -20xz + 35xz = 15xz
(15xz + 28x2 + -25z2) = 0

Solving
15xz + 28x2 + -25z2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + -5z)' equal to zero and attempt to solve:

Simplifying
7x + -5z = 0

Solving
7x + -5z = 0

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

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

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

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

Simplifying
x = 0.7142857143z

Subproblem 2
Set the factor '(4x + 5z)' equal to zero and attempt to solve:

Simplifying
4x + 5z = 0

Solving
4x + 5z = 0

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

Add '-5z' to each side of the equation.
4x + 5z + -5z = 0 + -5z

Combine like terms: 5z + -5z = 0
4x + 0 = 0 + -5z
4x = 0 + -5z
Remove the zero:
4x = -5z

Divide each side by '4'.
x = -1.25z

Simplifying
x = -1.25z
Solution
x = {0.7142857143z, -1.25z}

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