Solve (2x+3)(x-1)=x^2-ax+3

$$( 2 x + 3 ) ( x - 1 ) = x ^ { 2 } - a x + 3$$

Solve for a

$$a=-x-1+\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+3 by x-1 and combine like terms.

$$2x^{2}+x-3=x^{2}-ax+3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-ax+3=2x^{2}+x-3$$

Subtract x^{2} from both sides.

$$-ax+3=2x^{2}+x-3-x^{2}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$-ax+3=x^{2}+x-3$$

Subtract 3 from both sides.

$$-ax=x^{2}+x-3-3$$

Subtract 3 from -3 to get -6.

$$-ax=x^{2}+x-6$$

The equation is in standard form.

$$\left(-x\right)a=x^{2}+x-6$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{\left(x-2\right)\left(x+3\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{\left(x-2\right)\left(x+3\right)}{-x}$$

Divide \left(-2+x\right)\left(3+x\right) by -x.

$$a=-x-1+\frac{6}{x}$$

Solve for x

$$x=\frac{\sqrt{a^{2}+2a+25}-a-1}{2}$$

$$x=\frac{-\sqrt{a^{2}+2a+25}-a-1}{2}$$