3z*3z-8z+5-z*z+7z-12=

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Solution for 3z*3z-8z+5-z*z+7z-12= equation: 


Simplifying
3z * 3z + -8z + 5 + -1z * z + 7z + -12 = 0

Reorder the terms for easier multiplication:
3 * 3z * z + -8z + 5 + -1z * z + 7z + -12 = 0

Multiply 3 * 3
9z * z + -8z + 5 + -1z * z + 7z + -12 = 0

Multiply z * z
9z2 + -8z + 5 + -1z * z + 7z + -12 = 0

Multiply z * z
9z2 + -8z + 5 + -1z2 + 7z + -12 = 0

Reorder the terms:
5 + -12 + -8z + 7z + 9z2 + -1z2 = 0

Combine like terms: 5 + -12 = -7
-7 + -8z + 7z + 9z2 + -1z2 = 0

Combine like terms: -8z + 7z = -1z
-7 + -1z + 9z2 + -1z2 = 0

Combine like terms: 9z2 + -1z2 = 8z2
-7 + -1z + 8z2 = 0

Solving
-7 + -1z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -8z)(1 + -1z) = 0


Subproblem 1
Set the factor '(-7 + -8z)' equal to zero and attempt to solve:

Simplifying
-7 + -8z = 0

Solving
-7 + -8z = 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 + -8z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8z = 0 + 7
-8z = 0 + 7

Combine like terms: 0 + 7 = 7
-8z = 7

Divide each side by '-8'.
z = -0.875

Simplifying
z = -0.875

Subproblem 2
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
Solution
z = {-0.875, 1}

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