10z+4=z(5z+8)-12

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Solution for 10z+4=z(5z+8)-12 equation:


Simplifying
10z + 4 = z(5z + 8) + -12

Reorder the terms:
4 + 10z = z(5z + 8) + -12

Reorder the terms:
4 + 10z = z(8 + 5z) + -12
4 + 10z = (8 * z + 5z * z) + -12
4 + 10z = (8z + 5z2) + -12

Reorder the terms:
4 + 10z = -12 + 8z + 5z2

Solving
4 + 10z = -12 + 8z + 5z2

Solving for variable 'z'.

Reorder the terms:
4 + 12 + 10z + -8z + -5z2 = -12 + 8z + 5z2 + 12 + -8z + -5z2

Combine like terms: 4 + 12 = 16
16 + 10z + -8z + -5z2 = -12 + 8z + 5z2 + 12 + -8z + -5z2

Combine like terms: 10z + -8z = 2z
16 + 2z + -5z2 = -12 + 8z + 5z2 + 12 + -8z + -5z2

Reorder the terms:
16 + 2z + -5z2 = -12 + 12 + 8z + -8z + 5z2 + -5z2

Combine like terms: -12 + 12 = 0
16 + 2z + -5z2 = 0 + 8z + -8z + 5z2 + -5z2
16 + 2z + -5z2 = 8z + -8z + 5z2 + -5z2

Combine like terms: 8z + -8z = 0
16 + 2z + -5z2 = 0 + 5z2 + -5z2
16 + 2z + -5z2 = 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
16 + 2z + -5z2 = 0

Factor a trinomial.
(2 + -1z)(8 + 5z) = 0


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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2

Subproblem 2
Set the factor '(8 + 5z)' equal to zero and attempt to solve:

Simplifying
8 + 5z = 0

Solving
8 + 5z = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5z = 0 + -8
5z = 0 + -8

Combine like terms: 0 + -8 = -8
5z = -8

Divide each side by '5'.
z = -1.6

Simplifying
z = -1.6
Solution
z = {2, -1.6}

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