SOLUTION: Solve this equation (x+5)(x-4)(x+2)>0 Also: solve for x 4x(x-7)-5x(x-6)=-3 add: (2x^2-5xy+y^2)+(-9x^2-2xy-y^2)+(x^2+xy-2y^2) I have been working on these problems for q

Question 392450: Solve this equation
(x+5)(x-4)(x+2)>0
Also: solve for x
4x(x-7)-5x(x-6)=-3
add:
(2x^2-5xy+y^2)+(-9x^2-2xy-y^2)+(x^2+xy-2y^2)
I have been working on these problems for quite some time. thanks in advance!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(x+5)(x-4)(x+2)>0
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Draw a number line and plot x = -5,-2, and 4
---
Check a value from each of the resulting intervals
to see where the solution set is.
---
If x= -10 you get -*-*- > 0; false
---
If x = -3, you get +*-*- > 0; true, so solutions in (-5,-2)
---
If x = 0, you get +*-*+ > 0; false
---
If x = 10, you get +*+*+ > 0; true, solutions in (4,+inf)
=============
Ans: (-5,-2)U(4,+inf)
=======================================

Also: solve for x
4x(x-7)-5x(x-6)=-3
4x^2-28-5x^2+30x = -3
---
-x^2+30x-25 = 0
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x^2-30x+25 = 0
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x = [30 +- sqrt(900-4*25)]/2
---
x = [30 +- sqrt(800)]/2
---
x = [30 +- 20sqrt(2)]/2
---
x = [15 +- 10sqrt(2)]
=============================

Add:
(2x^2-5xy+y^2)+(-9x^2-2xy-y^2)+(x^2+xy-2y^2)
---
= -6x^2-6xy-2y^2
---
= -2(3x^2+3xy+y^2)
======================
Cheers,
Stan H.

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