8=4z-3z^2+15

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Solution for 8=4z-3z^2+15 equation: 


Simplifying
8 = 4z + -3z2 + 15

Reorder the terms:
8 = 15 + 4z + -3z2

Solving
8 = 15 + 4z + -3z2

Solving for variable 'z'.

Combine like terms: 8 + -15 = -7
-7 + -4z + 3z2 = 15 + 4z + -3z2 + -15 + -4z + 3z2

Reorder the terms:
-7 + -4z + 3z2 = 15 + -15 + 4z + -4z + -3z2 + 3z2

Combine like terms: 15 + -15 = 0
-7 + -4z + 3z2 = 0 + 4z + -4z + -3z2 + 3z2
-7 + -4z + 3z2 = 4z + -4z + -3z2 + 3z2

Combine like terms: 4z + -4z = 0
-7 + -4z + 3z2 = 0 + -3z2 + 3z2
-7 + -4z + 3z2 = -3z2 + 3z2

Combine like terms: -3z2 + 3z2 = 0
-7 + -4z + 3z2 = 0

Factor a trinomial.
(-1 + -1z)(7 + -3z) = 0


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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

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

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

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

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

Simplifying
z = -1

Subproblem 2
Set the factor '(7 + -3z)' equal to zero and attempt to solve:

Simplifying
7 + -3z = 0

Solving
7 + -3z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3z = 0 + -7
-3z = 0 + -7

Combine like terms: 0 + -7 = -7
-3z = -7

Divide each side by '-3'.
z = 2.333333333

Simplifying
z = 2.333333333
Solution
z = {-1, 2.333333333}

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