Solve for x 2(4x-1)+3(3-2x)=0

$2 (4 x - 1) + 3 (3 - 2 x) = 0$

Step 1

Simplify $2 (4 x - 1) + 3 (3 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$2 (4 x) + 2 \cdot - 1 + 3 (3 - 2 x) = 0$

Multiply $4$ by $2$ .

$8 x + 2 \cdot - 1 + 3 (3 - 2 x) = 0$

Multiply $2$ by $- 1$ .

$8 x - 2 + 3 (3 - 2 x) = 0$

Apply the distributive property.

$8 x - 2 + 3 \cdot 3 + 3 (- 2 x) = 0$

Multiply $3$ by $3$ .

$8 x - 2 + 9 + 3 (- 2 x) = 0$

Multiply $- 2$ by $3$ .

$8 x - 2 + 9 - 6 x = 0$

$8 x - 2 + 9 - 6 x = 0$

Simplify by adding terms.

Subtract $6 x$ from $8 x$ .

$2 x - 2 + 9 = 0$

Add $- 2$ and $9$ .

$2 x + 7 = 0$

$2 x + 7 = 0$

$2 x + 7 = 0$

Step 2

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Step 3

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

$x = \frac{- 7}{2}$

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

$x = - \frac{7}{2}$

$x = - \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{2}$

Decimal Form:

$x = - 3.5$

Mixed Number Form:

$x = - 3 \frac{1}{2}$

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