(5x-3z)(6x+7z)=

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Solution for (5x-3z)(6x+7z)= equation: 


Simplifying
(5x + -3z)(6x + 7z) = 0

Multiply (5x + -3z) * (6x + 7z)
(5x * (6x + 7z) + -3z * (6x + 7z)) = 0
((6x * 5x + 7z * 5x) + -3z * (6x + 7z)) = 0

Reorder the terms:
((35xz + 30x2) + -3z * (6x + 7z)) = 0
((35xz + 30x2) + -3z * (6x + 7z)) = 0
(35xz + 30x2 + (6x * -3z + 7z * -3z)) = 0
(35xz + 30x2 + (-18xz + -21z2)) = 0

Reorder the terms:
(35xz + -18xz + 30x2 + -21z2) = 0

Combine like terms: 35xz + -18xz = 17xz
(17xz + 30x2 + -21z2) = 0

Solving
17xz + 30x2 + -21z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -3z)(6x + 7z) = 0


Subproblem 1
Set the factor '(5x + -3z)' equal to zero and attempt to solve:

Simplifying
5x + -3z = 0

Solving
5x + -3z = 0

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

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

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

Divide each side by '5'.
x = 0.6z

Simplifying
x = 0.6z

Subproblem 2
Set the factor '(6x + 7z)' equal to zero and attempt to solve:

Simplifying
6x + 7z = 0

Solving
6x + 7z = 0

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

Add '-7z' to each side of the equation.
6x + 7z + -7z = 0 + -7z

Combine like terms: 7z + -7z = 0
6x + 0 = 0 + -7z
6x = 0 + -7z
Remove the zero:
6x = -7z

Divide each side by '6'.
x = -1.166666667z

Simplifying
x = -1.166666667z
Solution
x = {0.6z, -1.166666667z}

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