Solve f(a+h)-F(a)=7-6x+4x^2

$$f ( a + h ) - F ( a ) = 7 - 6 x + 4 x ^ { 2 }$$

Solve for F

$$\left\{\begin{matrix}F=\frac{-4x^{2}+6x+af+fh-7}{a}\text{, }&a\neq 0\\F\in \mathrm{R}\text{, }&f=-\frac{-4x^{2}+6x-7}{h}\text{ and }a=0\text{ and }h\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by a+h.

$$fa+fh-Fa=7-6x+4x^{2}$$

Subtract fa from both sides.

$$fh-Fa=7-6x+4x^{2}-fa$$

Subtract fh from both sides.

$$-Fa=7-6x+4x^{2}-fa-fh$$

The equation is in standard form.

$$\left(-a\right)F=4x^{2}-6x-af-fh+7$$

Divide both sides by -a.

$$\frac{\left(-a\right)F}{-a}=\frac{4x^{2}-6x-af-fh+7}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$F=\frac{4x^{2}-6x-af-fh+7}{-a}$$

Divide 7-6x+4x^{2}-fa-fh by -a.

$$F=-\frac{4x^{2}-6x-af-fh+7}{a}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{-4x^{2}+6x+fh-7}{f-F}\text{, }&f\neq F\\a\in \mathrm{R}\text{, }&f=\frac{4x^{2}-6x+7}{h}\text{ and }F=\frac{4x^{2}-6x+7}{h}\text{ and }h\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by a+h.

$$fa+fh-Fa=7-6x+4x^{2}$$

Subtract fh from both sides.

$$fa-Fa=7-6x+4x^{2}-fh$$

Combine all terms containing a.

$$\left(f-F\right)a=7-6x+4x^{2}-fh$$

The equation is in standard form.

$$\left(f-F\right)a=4x^{2}-6x-fh+7$$

Divide both sides by f-F.

$$\frac{\left(f-F\right)a}{f-F}=\frac{4x^{2}-6x-fh+7}{f-F}$$

Dividing by f-F undoes the multiplication by f-F.

$$a=\frac{4x^{2}-6x-fh+7}{f-F}$$