Choose the variable term to move—to avoid negative terms choose [latex]2x[/latex]

[latex]\,\,\,4x-6=2x+10\\\underline{-2x\,\,\,\,\,\,\,\,\,\,-2x}\\\,\,\,4x-6=10[/latex]

Now add 6 to both sides to isolate the term with the variable.

[latex]\begin{array}{r}4x-6=10\\\underline{\,\,\,\,+6\,\,\,+6}\\2x=16\end{array}[/latex]

Now divide each side by 2 to isolate the variable x.

[latex]\begin{array}{c}\dfrac{2x}{2}\normalsize=\dfrac{16}{2}\\\\\normalsize{x=8}\end{array}[/latex]

The equation is already set equal to zero, so we factor. The factored form of the equation is:

[latex]\left(x - 2\right)\left(x+3\right)=0[/latex]

Now, set each factor equal to zero and solve.

[latex]\begin{array}{l}\left(x - 2\right)\left(x+3\right)=0\hfill \\ \left(x - 2\right)=0\hfill \\ x=2\hfill \\ \left(x+3\right)=0\hfill \\ x=-3\hfill \end{array}[/latex]

The two solutions are [latex]x=2[/latex] and [latex]x=-3[/latex].

The equation is already set equal to zero, but [latex]a \ne{1}[/latex] so we need to split the middle term to help with grouping:

[latex]\left(8x^{2} +6x\right)+\left(-4x-3\right)=0[/latex]

Next we will pull out the GCF in each term:

[latex]2x\left(4x +3\right)+(-1)\left(4x+3\right)=0[/latex]

Then we will factor the equation:

[latex]\left(4x +3\right)+\left(2x-1\right)=0[/latex]

Now, set each factor equal to zero and solve.

[latex]\begin{array}{l} \left(4x +3\right)=0\hfill \\ 4x=-3\hfill \\ x=-\frac{3}{4}\hfill \\ \hfill \\ \left(2x-1\right)=0\hfill \\ 2x=1\hfill \\ x=\frac{1}{2}\hfill \end{array}[/latex]

The two solutions are [latex]x=-\dfrac{3}{4}[/latex] and [latex]x=\dfrac{1}{2}[/latex].

Take the square root of both sides, and then simplify the radical. Remember to use a [latex]\pm [/latex] sign before the radical symbol.

The solutions are [latex]x=2\sqrt{2}[/latex], [latex]x=-2\sqrt{2}[/latex].

First, isolate the [latex]{x}^{2}[/latex] term. Then take the square root of both sides.

The solutions are [latex]x=\frac{\sqrt{6}}{2}[/latex], [latex]x=-\frac{\sqrt{6}}{2}[/latex].