# Solve Equations with trinomials

#### Princezz3286

##### Junior Member
66) (z + 2)^2 = -z (3z + 4) + 9
(z + 2) (z + 2) = -z (3z + 4) + 9
(z + 2) (z + 2) = (-3z^2 - 4z + 9) * -1
(z + 2) (z + 2) = 3z^2 + 4z - 9
above is my work process, but this is where I am stuck because I can't factor 3z^2 + 4z - 9.... please let me know where to go from here.

70) 15t^3 + 40t = 70t^2
-70t^2 = -70t^2
------------------------------------
15t^3 - 70t^2 + 40t = 0
5t(3t^2 - 14t + 8) = 0
5t[(3t - 2)(t - 4)]= 0

where do I go from here? I don't get it?
HELP Thank You!
Heather

#### stapel

##### Super Moderator
Staff member
It looks as though your book and the classroom lecture skipped a very important concept! :shock:

. . . . .You must have the factors on one side of the equation, with "= 0"
. . . . .on the other side of the equation, in order to solve by factoring.

Princezz3286 said:
66) (z + 2)^2 = -z (3z + 4) + 9
Multiply out, move everything to one side, and only then factor!

. . . . .(z + 2)[sup:5ylmokkj]2[/sup:5ylmokkj] = -z(3z + 4) + 9

. . . . .z[sup:5ylmokkj]2[/sup:5ylmokkj] + 4z + 4 = -3z[sup:5ylmokkj]2[/sup:5ylmokkj] - 4z + 9

. . . . .z[sup:5ylmokkj]2[/sup:5ylmokkj] + 3z[sup:5ylmokkj]2[/sup:5ylmokkj] + 4z + 4z + 4 - 9 = 0

. . . . .4z[sup:5ylmokkj]2[/sup:5ylmokkj] + 8z - 5 = 0

Now find factors of (4)(-5) = -20 that are eight units apart.

Princezz3286 said:
5t[(3t - 2)(t - 4)]= 0

where do I go from here?
The only way the product can equal zero is if at least one factor equals zero. So set each factor equal to zero, and solve. Eliz.

#### Princezz3286

##### Junior Member
Thank you for your help on this! ##### New member
Consider the function y = 2x^-4x+9.
a) Minimum value?
b) Equation of axis of symmetry?

This is a question on a mock test that a student needs to solve and practice for a test on Monday. Any help for completing the squares would be much appreciated. Thank you.

Byron

#### Subhotosh Khan

##### Super Moderator
Staff member
Consider the function y = 2x^-4x+9.
a) Minimum value?
b) Equation of axis of symmetry?

This is a question on a mock test that a student needs to solve and practice for a test on Monday. Any help for completing the squares would be much appreciated. Thank you.

Byron
You shold start a new thread with new problem (by clicking new topic button)