2z(z+3)+15=3(z^2-6)-2z

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Solution for 2z(z+3)+15=3(z^2-6)-2z equation: 


Simplifying
2z(z + 3) + 15 = 3(z2 + -6) + -2z

Reorder the terms:
2z(3 + z) + 15 = 3(z2 + -6) + -2z
(3 * 2z + z * 2z) + 15 = 3(z2 + -6) + -2z
(6z + 2z2) + 15 = 3(z2 + -6) + -2z

Reorder the terms:
15 + 6z + 2z2 = 3(z2 + -6) + -2z

Reorder the terms:
15 + 6z + 2z2 = 3(-6 + z2) + -2z
15 + 6z + 2z2 = (-6 * 3 + z2 * 3) + -2z
15 + 6z + 2z2 = (-18 + 3z2) + -2z

Reorder the terms:
15 + 6z + 2z2 = -18 + -2z + 3z2

Solving
15 + 6z + 2z2 = -18 + -2z + 3z2

Solving for variable 'z'.

Reorder the terms:
15 + 18 + 6z + 2z + 2z2 + -3z2 = -18 + -2z + 3z2 + 18 + 2z + -3z2

Combine like terms: 15 + 18 = 33
33 + 6z + 2z + 2z2 + -3z2 = -18 + -2z + 3z2 + 18 + 2z + -3z2

Combine like terms: 6z + 2z = 8z
33 + 8z + 2z2 + -3z2 = -18 + -2z + 3z2 + 18 + 2z + -3z2

Combine like terms: 2z2 + -3z2 = -1z2
33 + 8z + -1z2 = -18 + -2z + 3z2 + 18 + 2z + -3z2

Reorder the terms:
33 + 8z + -1z2 = -18 + 18 + -2z + 2z + 3z2 + -3z2

Combine like terms: -18 + 18 = 0
33 + 8z + -1z2 = 0 + -2z + 2z + 3z2 + -3z2
33 + 8z + -1z2 = -2z + 2z + 3z2 + -3z2

Combine like terms: -2z + 2z = 0
33 + 8z + -1z2 = 0 + 3z2 + -3z2
33 + 8z + -1z2 = 3z2 + -3z2

Combine like terms: 3z2 + -3z2 = 0
33 + 8z + -1z2 = 0

Factor a trinomial.
(11 + -1z)(3 + z) = 0


Subproblem 1
Set the factor '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11

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

Simplifying
3 + z = 0

Solving
3 + z = 0

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

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

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

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

Simplifying
z = -3
Solution
z = {11, -3}

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