Solve the equation (2x- 3)(x+5)=15?

Solve the equation:

(2x - 3)(x + 5) = 15

Multiply using the FOIL Method

2x * x = 2x^2

2x * 5 = 10x

-3 * x = -3x

-3 * 5 = -15

2x^2 + 10x - 3x - 15

Combine like terms:

10x - 3x = 7x

2x^2 + 7x - 15 = 15

Add -15 to each side of the equation

2x^2 + 7x - 15 - 15 = 15 -15

Combine like terms:

-15 + -15 = -30

15 + -15 = 0

2x^2 + 7x - 30 = 0

Factor a trinomial

(1x + 6)(2x - 5) = 0

Subproblem 1

x + 6 = 0

Add -6 to each side of the equation

x + 6 - 6 = 0 - 6

x = -6

Subproblem 2

2x - 5 = 0

Add 5 to each side of the equation

2x - 5 + 5 = 0 + 5

2x = 5

Divide each side by 2

2x/2 = 5/2

x = 2.5

Solution:

x = -6, 2.5

For your information:

R.R above is wrong.

2x² + 7x - 15 = 15
2x² + 7x - 30 = 0
2x² + 12x - 5x - 30 = 0
2x(x + 6) - 5(x + 6) = 0
(2x - 5)(x + 6) = 0
x = 5/2 or x = -6

2x^2 + 7x -30 = 0

Differentiating above quadratic equation, we get
2x +7 = 0

x = -3.5

2x² + 10x -3x - 15 = 15
2x² + 7x - 30 = 0
Using the quadratic formula you get,

x = 2.5
x = -6

Multiply out the brackets
2x^2 + 10x - 3x - 15 = 15
2x^2 + 7x - 30 = 0
(2x - 5)(x + 6) = 0
x = 5/2, -6

2/[x(x + 1)] - 1/(2x) = (3 - x)/[2x(x + 1)]

1)
(2x - 3)(x + 5) = 15
2x*x + 2x*5 - 3*x - 3*5 = 15
2x^2 + 10x - 3x - 15 = 15
2x^2 + 7x - 15 - 15 = 0
2x^2 + 7x - 30 = 0
2x^2 + 12x - 5x - 30 = 0
(2x^2 + 12x) - (5x + 30) = 0
2x(x + 6) - 5(x + 6) = 0
(x + 6)(2x - 5) = 0

x + 6 = 0
x = -6

2x - 5 = 0
2x = 5
x = 5/2 (2.5)

∴ x = -6, 5/2 (2.5)

= = = = = = = = = = = = = = = =

2)
2/[x(x + 1)] - 1/(2x)
= (2 * 2)/[2 * x(x + 1)] - [1 * (x + 1)]/[(x + 1) * 2x]
= 4/[2x(x + 1)] - (x + 1)/[2x(x + 1)]
= [4 - (x + 1)]/[2x(x + 1)]
= (4 - x - 1)/[2x(x + 1)]
= (-x + 3)/[2x(x + 1)]

2 x ² + 7 x - 30 = 0
( 2 x - 5 ) ( x + 6 ) = 0
x = 5/2 , x = - 6

For the benefit of R R, if we differentiate the equation, we get
4x +7 = 0.
But that's got nothing to do with it any way.

2/x(x+1) - 1/2x = 2/2x(x+1) - (x+1)/2x(x+1)
=(2-x-1)/2x(x+1)
= (1-x)/2x(x+1)