Solve left(6-aright)x-20=-005x^2+10x-40

$$\left( 6-a \right) x-20 = -005 { x }^{ 2 } +10x-40$$

Solve for a

$$a=-4+\frac{20}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6-a by x.

$$6x-ax-20=0\times 0\times 5x^{2}+10x-40$$

Multiply 0 and 0 to get 0.

$$6x-ax-20=0\times 5x^{2}+10x-40$$

Multiply 0 and 5 to get 0.

$$6x-ax-20=0x^{2}+10x-40$$

Anything times zero gives zero.

$$6x-ax-20=0+10x-40$$

Subtract 40 from 0 to get -40.

$$6x-ax-20=-40+10x$$

Subtract 6x from both sides.

$$-ax-20=-40+10x-6x$$

Combine 10x and -6x to get 4x.

$$-ax-20=-40+4x$$

Add 20 to both sides.

$$-ax=-40+4x+20$$

Add -40 and 20 to get -20.

$$-ax=-20+4x$$

The equation is in standard form.

$$\left(-x\right)a=4x-20$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{4x-20}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{4x-20}{-x}$$

Divide -20+4x by -x.

$$a=-4+\frac{20}{x}$$

Solve for x

$$x=\frac{20}{a+4}$$

$$a\neq -4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6-a by x.

$$6x-ax-20=0\times 0\times 5x^{2}+10x-40$$

Multiply 0 and 0 to get 0.

$$6x-ax-20=0\times 5x^{2}+10x-40$$

Multiply 0 and 5 to get 0.

$$6x-ax-20=0x^{2}+10x-40$$

Anything times zero gives zero.

$$6x-ax-20=0+10x-40$$

Subtract 40 from 0 to get -40.

$$6x-ax-20=-40+10x$$

Subtract 10x from both sides.

$$6x-ax-20-10x=-40$$

Combine 6x and -10x to get -4x.

$$-4x-ax-20=-40$$

Add 20 to both sides.

$$-4x-ax=-40+20$$

Add -40 and 20 to get -20.

$$-4x-ax=-20$$

Combine all terms containing x.

$$\left(-4-a\right)x=-20$$

The equation is in standard form.

$$\left(-a-4\right)x=-20$$

Divide both sides by -4-a.

$$\frac{\left(-a-4\right)x}{-a-4}=-\frac{20}{-a-4}$$

Dividing by -4-a undoes the multiplication by -4-a.

$$x=-\frac{20}{-a-4}$$

Divide -20 by -4-a.

$$x=\frac{20}{a+4}$$