Solve for x 5(7x+1)+6=x(3-x)+2-x(7-x)

$5 (7 x + 1) + 6 = x (3 - x) + 2 - x (7 - x)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x (3 - x) + 2 - x (7 - x) = 5 (7 x + 1) + 6$

Step 2

Simplify $x (3 - x) + 2 - x (7 - x)$ .

Simplify each term.

Apply the distributive property.

$x \cdot 3 + x (- x) + 2 - x (7 - x) = 5 (7 x + 1) + 6$

Move $3$ to the left of $x$ .

$3 \cdot x + x (- x) + 2 - x (7 - x) = 5 (7 x + 1) + 6$

Rewrite using the commutative property of multiplication.

$3 \cdot x - x \cdot x + 2 - x (7 - x) = 5 (7 x + 1) + 6$

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

Move $x$ .

$3 x - (x \cdot x) + 2 - x (7 - x) = 5 (7 x + 1) + 6$

Multiply $x$ by $x$ .

$3 x - x^{2} + 2 - x (7 - x) = 5 (7 x + 1) + 6$

Apply the distributive property.

$3 x - x^{2} + 2 - x \cdot 7 - x (- x) = 5 (7 x + 1) + 6$

Multiply $7$ by $- 1$ .

$3 x - x^{2} + 2 - 7 x - x (- x) = 5 (7 x + 1) + 6$

Rewrite using the commutative property of multiplication.

$3 x - x^{2} + 2 - 7 x - 1 \cdot - 1 x \cdot x = 5 (7 x + 1) + 6$

Simplify each term.

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

Move $x$ .

$3 x - x^{2} + 2 - 7 x - 1 \cdot - 1 (x \cdot x) = 5 (7 x + 1) + 6$

Multiply $x$ by $x$ .

$3 x - x^{2} + 2 - 7 x - 1 \cdot - 1 x^{2} = 5 (7 x + 1) + 6$

Multiply $- 1$ by $- 1$ .

$3 x - x^{2} + 2 - 7 x + 1 x^{2} = 5 (7 x + 1) + 6$

Multiply $x^{2}$ by $1$ .

$3 x - x^{2} + 2 - 7 x + x^{2} = 5 (7 x + 1) + 6$

Simplify by adding terms.

Combine the opposite terms in $3 x - x^{2} + 2 - 7 x + x^{2}$ .

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

$3 x + 2 - 7 x + 0 = 5 (7 x + 1) + 6$

Add $3 x + 2 - 7 x$ and $0$ .

$3 x + 2 - 7 x = 5 (7 x + 1) + 6$

Subtract $7 x$ from $3 x$ .

$- 4 x + 2 = 5 (7 x + 1) + 6$

Step 3

Simplify $5 (7 x + 1) + 6$ .

Simplify each term.

Apply the distributive property.

$- 4 x + 2 = 5 (7 x) + 5 \cdot 1 + 6$

Multiply $7$ by $5$ .

$- 4 x + 2 = 35 x + 5 \cdot 1 + 6$

Multiply $5$ by $1$ .

$- 4 x + 2 = 35 x + 5 + 6$

Add $5$ and $6$ .

$- 4 x + 2 = 35 x + 11$

Step 4

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

Subtract $35 x$ from both sides of the equation.

$- 4 x + 2 - 35 x = 11$

Subtract $35 x$ from $- 4 x$ .

$- 39 x + 2 = 11$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- 39 x = 11 - 2$

Subtract $2$ from $11$ .

$- 39 x = 9$

Step 6

Divide each term in $- 39 x = 9$ by $- 39$ and simplify.

Divide each term in $- 39 x = 9$ by $- 39$ .

$\frac{- 39 x}{- 39} = \frac{9}{- 39}$

Simplify the left side.

Cancel the common factor of $- 39$ .

Cancel the common factor.

$\frac{- 39 x}{- 39} = \frac{9}{- 39}$

Divide $x$ by $1$ .

$x = \frac{9}{- 39}$

Simplify the right side.

Cancel the common factor of $9$ and $- 39$ .

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{- 39}$

Cancel the common factors.

Factor $3$ out of $- 39$ .

$x = \frac{3 \cdot 3}{3 \cdot - 13}$

Cancel the common factor.

$x = \frac{3 \cdot 3}{3 \cdot - 13}$

Rewrite the expression.

$x = \frac{3}{- 13}$

Move the negative in front of the fraction.

$x = - \frac{3}{13}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{13}$

Decimal Form:

$x = - 0.\overline{230769}$

Solve for x 5(7x+1)+6=x(3-x)+2-x(7-x)

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