6z(3z+2)+7z(2z-3)=32z+10z

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Solution for 6z(3z+2)+7z(2z-3)=32z+10z equation: 


Simplifying
6z(3z + 2) + 7z(2z + -3) = 32z + 10z

Reorder the terms:
6z(2 + 3z) + 7z(2z + -3) = 32z + 10z
(2 * 6z + 3z * 6z) + 7z(2z + -3) = 32z + 10z
(12z + 18z2) + 7z(2z + -3) = 32z + 10z

Reorder the terms:
12z + 18z2 + 7z(-3 + 2z) = 32z + 10z
12z + 18z2 + (-3 * 7z + 2z * 7z) = 32z + 10z
12z + 18z2 + (-21z + 14z2) = 32z + 10z

Reorder the terms:
12z + -21z + 18z2 + 14z2 = 32z + 10z

Combine like terms: 12z + -21z = -9z
-9z + 18z2 + 14z2 = 32z + 10z

Combine like terms: 18z2 + 14z2 = 32z2
-9z + 32z2 = 32z + 10z

Combine like terms: 32z + 10z = 42z
-9z + 32z2 = 42z

Solving
-9z + 32z2 = 42z

Solving for variable 'z'.

Reorder the terms:
-9z + -42z + 32z2 = 42z + -42z

Combine like terms: -9z + -42z = -51z
-51z + 32z2 = 42z + -42z

Combine like terms: 42z + -42z = 0
-51z + 32z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-51 + 32z) = 0


Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

Subproblem 2
Set the factor '(-51 + 32z)' equal to zero and attempt to solve:

Simplifying
-51 + 32z = 0

Solving
-51 + 32z = 0

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

Add '51' to each side of the equation.
-51 + 51 + 32z = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 32z = 0 + 51
32z = 0 + 51

Combine like terms: 0 + 51 = 51
32z = 51

Divide each side by '32'.
z = 1.59375

Simplifying
z = 1.59375
Solution
z = {0, 1.59375}

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