If (2x+3)(ax-5) = 12x^2+bx-15 for all values of x, what is the value of b?

step  1  :

Equation at the end of step  1  :

((2x + 3) • (xa - 5)) -  (((22•3x2) +  xb) -  15)  = 0  

Step  2  :

Equation at the end of step  2  :

(2x + 3) • (xa - 5) -  (12x2 + xb - 15)  = 0  

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

 2x2a - 12x2 + 3xa - xb - 10x  =  

x • (2xa - 12x + 3a - b - 10)  

Equation at the end of step  4  :

x • (2xa - 12x + 3a - b - 10)  = 0  

Step  5  :

Theory - Roots of a product :

5.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

5.2      Solve  :    x = 0  

Solution is  x = 0

Solving a Single Variable Equation :

5.3     Solve   2xa-12x+3a-b-10  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

One solution was found :

                 x = 0

Step-by-step explanation:

true

explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .