Question 1103691
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<pre>
Take square root from both sides.


Then your original equation deploys in TWO independent equations:


1)  4x + 3 = 2   ====>  4x = 2 - 3 = -1   ====>  x = {{{(-1)/4}}} = {{{-1/4}}} = -0.25.


2)  4x + 3 = -2  ====>  4x = -2 - 3 = -5  ====>  x = {{{(-5)/4}}} = {{{-5/4}}} = -1.25.


<U>Answer</U>. Two solutions are  x= -0.25  and  x= -1.25.
</pre>


There are many ways (more than one way) to reduce the original equations to linear equations 1) and 2).


All these ways lead to the same set of solutions.




Visually, this plot might be helpful:



{{{graph( 330, 330, -3.5, 2.5, -2.5, 10.5,
          (4x+3)^2, 4
)}}}


Plot y = {{{(4x+3)^2}}} (red) and y = 4 (green)