Solve for x x^2+x(6-2x)=(x-1)(2-x)-2

$x^{2} + x (6 - 2 x) = (x - 1) (2 - x) - 2$

Step 1

Simplify $x^{2} + x (6 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$x^{2} + x \cdot 6 + x (- 2 x) = (x - 1) (2 - x) - 2$

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x + x (- 2 x) = (x - 1) (2 - x) - 2$

Rewrite using the commutative property of multiplication.

$x^{2} + 6 \cdot x - 2 x \cdot x = (x - 1) (2 - x) - 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{2} + 6 x - 2 (x \cdot x) = (x - 1) (2 - x) - 2$

Multiply $x$ by $x$ .

$x^{2} + 6 x - 2 x^{2} = (x - 1) (2 - x) - 2$

Subtract $2 x^{2}$ from $x^{2}$ .

$- x^{2} + 6 x = (x - 1) (2 - x) - 2$

Step 2

Simplify $(x - 1) (2 - x) - 2$ .

Simplify each term.

Expand $(x - 1) (2 - x)$ using the FOIL Method.

Apply the distributive property.

$- x^{2} + 6 x = x (2 - x) - 1 (2 - x) - 2$

Apply the distributive property.

$- x^{2} + 6 x = x \cdot 2 + x (- x) - 1 (2 - x) - 2$

Apply the distributive property.

$- x^{2} + 6 x = x \cdot 2 + x (- x) - 1 \cdot 2 - 1 (- x) - 2$

Simplify and combine like terms.

Simplify each term.

Move $2$ to the left of $x$ .

$- x^{2} + 6 x = 2 \cdot x + x (- x) - 1 \cdot 2 - 1 (- x) - 2$

Rewrite using the commutative property of multiplication.

$- x^{2} + 6 x = 2 x - x \cdot x - 1 \cdot 2 - 1 (- x) - 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- x^{2} + 6 x = 2 x - (x \cdot x) - 1 \cdot 2 - 1 (- x) - 2$

Multiply $x$ by $x$ .

$- x^{2} + 6 x = 2 x - x^{2} - 1 \cdot 2 - 1 (- x) - 2$

Multiply $- 1$ by $2$ .

$- x^{2} + 6 x = 2 x - x^{2} - 2 - 1 (- x) - 2$

Multiply $- 1 (- x)$ .

Multiply $- 1$ by $- 1$ .

$- x^{2} + 6 x = 2 x - x^{2} - 2 + 1 x - 2$

Multiply $x$ by $1$ .

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

Add $2 x$ and $x$ .

$- x^{2} + 6 x = 3 x - x^{2} - 2 - 2$

Subtract $2$ from $- 2$ .

$- x^{2} + 6 x = 3 x - x^{2} - 4$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$- x^{2} + 6 x - 3 x = - x^{2} - 4$

Add $x^{2}$ to both sides of the equation.

$- x^{2} + 6 x - 3 x + x^{2} = - 4$

Combine the opposite terms in $- x^{2} + 6 x - 3 x + x^{2}$ .

Add $- x^{2}$ and $x^{2}$ .

$6 x - 3 x + 0 = - 4$

Add $6 x - 3 x$ and $0$ .

$6 x - 3 x = - 4$

Subtract $3 x$ from $6 x$ .

$3 x = - 4$

Step 4

Divide each term in $3 x = - 4$ by $3$ and simplify.

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$

Solve for x x^2+x(6-2x)=(x-1)(2-x)-2

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