(3z+5)x(2z+7)=

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Solution for (3z+5)x(2z+7)= equation: 


Simplifying
(3z + 5) * x(2z + 7) = 0

Reorder the terms:
(5 + 3z) * x(2z + 7) = 0

Reorder the terms:
(5 + 3z) * x(7 + 2z) = 0

Reorder the terms for easier multiplication:
x(5 + 3z)(7 + 2z) = 0

Multiply (5 + 3z) * (7 + 2z)
x(5(7 + 2z) + 3z * (7 + 2z)) = 0
x((7 * 5 + 2z * 5) + 3z * (7 + 2z)) = 0
x((35 + 10z) + 3z * (7 + 2z)) = 0
x(35 + 10z + (7 * 3z + 2z * 3z)) = 0
x(35 + 10z + (21z + 6z2)) = 0

Combine like terms: 10z + 21z = 31z
x(35 + 31z + 6z2) = 0
(35 * x + 31z * x + 6z2 * x) = 0
(35x + 31xz + 6xz2) = 0

Solving
35x + 31xz + 6xz2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(35 + 31z + 6z2) = 0

Factor a trinomial.
x((7 + 2z)(5 + 3z)) = 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 '(7 + 2z)' equal to zero and attempt to solve:

Simplifying
7 + 2z = 0

Solving
7 + 2z = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2z = 0 + -7
2z = 0 + -7

Combine like terms: 0 + -7 = -7
2z = -7

Add '-2z' to each side of the equation.
2z + -2z = -7 + -2z

Combine like terms: 2z + -2z = 0
0 = -7 + -2z

Simplifying
0 = -7 + -2z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
5 + 3z = 0

Solving
5 + 3z = 0

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

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

Combine like terms: 5 + -5 = 0
0 + 3z = 0 + -5
3z = 0 + -5

Combine like terms: 0 + -5 = -5
3z = -5

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

Combine like terms: 3z + -3z = 0
0 = -5 + -3z

Simplifying
0 = -5 + -3z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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