(3x+5z)(5x-7z)=

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


Simplifying
(3x + 5z)(5x + -7z) = 0

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

Reorder the terms:
((-21xz + 15x2) + 5z * (5x + -7z)) = 0
((-21xz + 15x2) + 5z * (5x + -7z)) = 0
(-21xz + 15x2 + (5x * 5z + -7z * 5z)) = 0
(-21xz + 15x2 + (25xz + -35z2)) = 0

Reorder the terms:
(-21xz + 25xz + 15x2 + -35z2) = 0

Combine like terms: -21xz + 25xz = 4xz
(4xz + 15x2 + -35z2) = 0

Solving
4xz + 15x2 + -35z2 = 0

Solving for variable 'x'.

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


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

Simplifying
5x + -7z = 0

Solving
5x + -7z = 0

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

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

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

Divide each side by '5'.
x = 1.4z

Simplifying
x = 1.4z

Subproblem 2
Set the factor '(3x + 5z)' equal to zero and attempt to solve:

Simplifying
3x + 5z = 0

Solving
3x + 5z = 0

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

Add '-5z' to each side of the equation.
3x + 5z + -5z = 0 + -5z

Combine like terms: 5z + -5z = 0
3x + 0 = 0 + -5z
3x = 0 + -5z
Remove the zero:
3x = -5z

Divide each side by '3'.
x = -1.666666667z

Simplifying
x = -1.666666667z
Solution
x = {1.4z, -1.666666667z}

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