7z^2+4z+23=6z^2+15z-7

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Solution for 7z^2+4z+23=6z^2+15z-7 equation: 


Simplifying
7z2 + 4z + 23 = 6z2 + 15z + -7

Reorder the terms:
23 + 4z + 7z2 = 6z2 + 15z + -7

Reorder the terms:
23 + 4z + 7z2 = -7 + 15z + 6z2

Solving
23 + 4z + 7z2 = -7 + 15z + 6z2

Solving for variable 'z'.

Reorder the terms:
23 + 7 + 4z + -15z + 7z2 + -6z2 = -7 + 15z + 6z2 + 7 + -15z + -6z2

Combine like terms: 23 + 7 = 30
30 + 4z + -15z + 7z2 + -6z2 = -7 + 15z + 6z2 + 7 + -15z + -6z2

Combine like terms: 4z + -15z = -11z
30 + -11z + 7z2 + -6z2 = -7 + 15z + 6z2 + 7 + -15z + -6z2

Combine like terms: 7z2 + -6z2 = 1z2
30 + -11z + 1z2 = -7 + 15z + 6z2 + 7 + -15z + -6z2

Reorder the terms:
30 + -11z + 1z2 = -7 + 7 + 15z + -15z + 6z2 + -6z2

Combine like terms: -7 + 7 = 0
30 + -11z + 1z2 = 0 + 15z + -15z + 6z2 + -6z2
30 + -11z + 1z2 = 15z + -15z + 6z2 + -6z2

Combine like terms: 15z + -15z = 0
30 + -11z + 1z2 = 0 + 6z2 + -6z2
30 + -11z + 1z2 = 6z2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
30 + -11z + 1z2 = 0

Factor a trinomial.
(5 + -1z)(6 + -1z) = 0


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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5

Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {5, 6}

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