185+z^2+18z+81=9(45+25-10z+z^2)

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Solution for 185+z^2+18z+81=9(45+25-10z+z^2) equation: 


Simplifying
185 + z2 + 18z + 81 = 9(45 + 25 + -10z + z2)

Reorder the terms:
185 + 81 + 18z + z2 = 9(45 + 25 + -10z + z2)

Combine like terms: 185 + 81 = 266
266 + 18z + z2 = 9(45 + 25 + -10z + z2)

Combine like terms: 45 + 25 = 70
266 + 18z + z2 = 9(70 + -10z + z2)
266 + 18z + z2 = (70 * 9 + -10z * 9 + z2 * 9)
266 + 18z + z2 = (630 + -90z + 9z2)

Solving
266 + 18z + z2 = 630 + -90z + 9z2

Solving for variable 'z'.

Reorder the terms:
266 + -630 + 18z + 90z + z2 + -9z2 = 630 + -90z + 9z2 + -630 + 90z + -9z2

Combine like terms: 266 + -630 = -364
-364 + 18z + 90z + z2 + -9z2 = 630 + -90z + 9z2 + -630 + 90z + -9z2

Combine like terms: 18z + 90z = 108z
-364 + 108z + z2 + -9z2 = 630 + -90z + 9z2 + -630 + 90z + -9z2

Combine like terms: z2 + -9z2 = -8z2
-364 + 108z + -8z2 = 630 + -90z + 9z2 + -630 + 90z + -9z2

Reorder the terms:
-364 + 108z + -8z2 = 630 + -630 + -90z + 90z + 9z2 + -9z2

Combine like terms: 630 + -630 = 0
-364 + 108z + -8z2 = 0 + -90z + 90z + 9z2 + -9z2
-364 + 108z + -8z2 = -90z + 90z + 9z2 + -9z2

Combine like terms: -90z + 90z = 0
-364 + 108z + -8z2 = 0 + 9z2 + -9z2
-364 + 108z + -8z2 = 9z2 + -9z2

Combine like terms: 9z2 + -9z2 = 0
-364 + 108z + -8z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-91 + 27z + -2z2) = 0

Factor a trinomial.
4((-7 + z)(13 + -2z)) = 0

Ignore the factor 4.

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

Simplifying
-7 + z = 0

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

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

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

Simplifying
z = 7

Subproblem 2
Set the factor '(13 + -2z)' equal to zero and attempt to solve:

Simplifying
13 + -2z = 0

Solving
13 + -2z = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2z = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2z = 0 + -13
-2z = 0 + -13

Combine like terms: 0 + -13 = -13
-2z = -13

Divide each side by '-2'.
z = 6.5

Simplifying
z = 6.5
Solution
z = {7, 6.5}

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