Solve for d d-7=(4d+3)/e

$d - 7 = \frac{4 d + 3}{e}$

Step 1

Multiply both sides by $e$ .

$(d - 7) e = \frac{4 d + 3}{e} e$

Step 2

Simplify.

Simplify the left side.

Apply the distributive property.

$d e - 7 e = \frac{4 d + 3}{e} e$

Simplify the right side.

Cancel the common factor of $e$ .

Cancel the common factor.

$d e - 7 e = \frac{4 d + 3}{e} e$

Rewrite the expression.

$d e - 7 e = 4 d + 3$

Step 3

Solve for $d$ .

Subtract $4 d$ from both sides of the equation.

$d e - 7 e - 4 d = 3$

Add $7 e$ to both sides of the equation.

$d e - 4 d = 3 + 7 e$

Factor $d$ out of $d e - 4 d$ .

Factor $d$ out of $d e$ .

$d (e) - 4 d = 3 + 7 e$

Factor $d$ out of $- 4 d$ .

$d (e) + d \cdot - 4 = 3 + 7 e$

Factor $d$ out of $d (e) + d \cdot - 4$ .

$d (e - 4) = 3 + 7 e$

Divide each term in $d (e - 4) = 3 + 7 e$ by $e - 4$ and simplify.

Divide each term in $d (e - 4) = 3 + 7 e$ by $e - 4$ .

$\frac{d (e - 4)}{e - 4} = \frac{3}{e - 4} + \frac{7 e}{e - 4}$

Simplify the left side.

Cancel the common factor of $e - 4$ .

Cancel the common factor.

$\frac{d (e - 4)}{e - 4} = \frac{3}{e - 4} + \frac{7 e}{e - 4}$

Divide $d$ by $1$ .

$d = \frac{3}{e - 4} + \frac{7 e}{e - 4}$

Simplify the right side.

Combine the numerators over the common denominator.

$d = \frac{3 + 7 e}{e - 4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = \frac{3 + 7 e}{e - 4}$

Decimal Form:

$d = - 17.18628423 \dots$

Solve for d d-7=(4d+3)/e

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