Solve for x 4(4+2x)-6(7x-10)=-80

$4 (4 + 2 x) - 6 (7 x - 10) = - 80$

Step 1

Simplify $4 (4 + 2 x) - 6 (7 x - 10)$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 4 + 4 (2 x) - 6 (7 x - 10) = - 80$

Multiply $4$ by $4$ .

$16 + 4 (2 x) - 6 (7 x - 10) = - 80$

Multiply $2$ by $4$ .

$16 + 8 x - 6 (7 x - 10) = - 80$

Apply the distributive property.

$16 + 8 x - 6 (7 x) - 6 \cdot - 10 = - 80$

Multiply $7$ by $- 6$ .

$16 + 8 x - 42 x - 6 \cdot - 10 = - 80$

Multiply $- 6$ by $- 10$ .

$16 + 8 x - 42 x + 60 = - 80$

$16 + 8 x - 42 x + 60 = - 80$

Simplify by adding terms.

Add $16$ and $60$ .

$8 x - 42 x + 76 = - 80$

Subtract $42 x$ from $8 x$ .

$- 34 x + 76 = - 80$

$- 34 x + 76 = - 80$

$- 34 x + 76 = - 80$

Step 2

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

Subtract $76$ from both sides of the equation.

$- 34 x = - 80 - 76$

Subtract $76$ from $- 80$ .

$- 34 x = - 156$

$- 34 x = - 156$

Step 3

Divide each term in $- 34 x = - 156$ by $- 34$ and simplify.

Divide each term in $- 34 x = - 156$ by $- 34$ .

$\frac{- 34 x}{- 34} = \frac{- 156}{- 34}$

Simplify the left side.

Cancel the common factor of $- 34$ .

Cancel the common factor.

$\frac{- 34 x}{- 34} = \frac{- 156}{- 34}$

Divide $x$ by $1$ .

$x = \frac{- 156}{- 34}$

$x = \frac{- 156}{- 34}$

$x = \frac{- 156}{- 34}$

Simplify the right side.

Cancel the common factor of $- 156$ and $- 34$ .

Factor $- 2$ out of $- 156$ .

$x = \frac{- 2 (78)}{- 34}$

Cancel the common factors.

Factor $- 2$ out of $- 34$ .

$x = \frac{- 2 \cdot 78}{- 2 \cdot 17}$

Cancel the common factor.

$x = \frac{- 2 \cdot 78}{- 2 \cdot 17}$

Rewrite the expression.

$x = \frac{78}{17}$

$x = \frac{78}{17}$

$x = \frac{78}{17}$

$x = \frac{78}{17}$

$x = \frac{78}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{78}{17}$

Decimal Form:

$x = 4.58823529 \dots$

Mixed Number Form:

$x = 4 \frac{10}{17}$

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