Question

Solve each of the following equation

Answer 1

`(2x+3)^2=(3x-1)^2`

start by expanding both sides of the equation

`\begin{gathered} (2x)^2+2\cdot2x\cdot3+3^2=(3x)^2-2\cdot3x\cdot1+1^2 \\ 4x^2+12x+9=9x^2-6x+1 \end{gathered}`

bring all to the left side of the equation

`\begin{gathered} 4x^2+12x+9-9x^2+6x-1=0 \\ -5x^2+18x+8=0 \end{gathered}`

switch the signs of the equations

`5x^2-18x-8=0`

write -18x as a difference

`5x^2+2x-20x-8=0`

factor x and factor -4

`x\cdot(5x+2)-4\cdot(5x+2)=0`

factor '5x+2' of the expression

`(5x+2)\cdot(x-4)=0`

when a product of two factors is equal to 0, at least one of the factors is 0, then equal each to 0 and solve for x

`\begin{gathered} 5x+2=0 \\ 5x=-2 \\ x=-(2)/(5) \\ \\ x-4=0 \\ x=4 \end{gathered}`

the solutions to the equation are 4 and -2/5.