Solve d=7-6d/d

$$d = \frac { 7 - 6 d } { d }$$

Solve for d

$$d=-7$$

$$d=1$$

Steps Using Factoring

Subtract \frac{7-6d}{d} from both sides.

$$d-\frac{7-6d}{d}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply d times \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Since \frac{dd}{d} and \frac{7-6d}{d} have the same denominator, subtract them by subtracting their numerators.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Do the multiplications in dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d.

$$d^{2}-7+6d=0$$

Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$d^{2}+6d-7=0$$

To solve the equation, factor d^{2}+6d-7 using formula d^{2}+\left(a+b\right)d+ab=\left(d+a\right)\left(d+b\right). To find a and b, set up a system to be solved.

$$a+b=6 ab=-7$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=7$$

Rewrite factored expression \left(d+a\right)\left(d+b\right) using the obtained values.

$$\left(d-1\right)\left(d+7\right)$$

To find equation solutions, solve d-1=0 and d+7=0.

$$d=1 d=-7$$

Steps Using Factoring By Grouping

Subtract \frac{7-6d}{d} from both sides.

$$d-\frac{7-6d}{d}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply d times \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Since \frac{dd}{d} and \frac{7-6d}{d} have the same denominator, subtract them by subtracting their numerators.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Do the multiplications in dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d.

$$d^{2}-7+6d=0$$

Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$d^{2}+6d-7=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as d^{2}+ad+bd-7. To find a and b, set up a system to be solved.

$$a+b=6 ab=1\left(-7\right)=-7$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=7$$

Rewrite d^{2}+6d-7 as \left(d^{2}-d\right)+\left(7d-7\right).

$$\left(d^{2}-d\right)+\left(7d-7\right)$$

Factor out d in the first and 7 in the second group.

$$d\left(d-1\right)+7\left(d-1\right)$$

Factor out common term d-1 by using distributive property.

$$\left(d-1\right)\left(d+7\right)$$

To find equation solutions, solve d-1=0 and d+7=0.

$$d=1 d=-7$$

Steps Using the Quadratic Formula

Subtract \frac{7-6d}{d} from both sides.

$$d-\frac{7-6d}{d}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply d times \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Since \frac{dd}{d} and \frac{7-6d}{d} have the same denominator, subtract them by subtracting their numerators.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Do the multiplications in dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d.

$$d^{2}-7+6d=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$d^{2}+6d-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{-6±\sqrt{6^{2}-4\left(-7\right)}}{2}$$

Square 6.

$$d=\frac{-6±\sqrt{36-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$d=\frac{-6±\sqrt{36+28}}{2}$$

Add 36 to 28.

$$d=\frac{-6±\sqrt{64}}{2}$$

Take the square root of 64.

$$d=\frac{-6±8}{2}$$

Now solve the equation d=\frac{-6±8}{2} when ± is plus. Add -6 to 8.

$$d=\frac{2}{2}$$

Divide 2 by 2.

$$d=1$$

Now solve the equation d=\frac{-6±8}{2} when ± is minus. Subtract 8 from -6.

$$d=-\frac{14}{2}$$

Divide -14 by 2.

$$d=-7$$

The equation is now solved.

$$d=1 d=-7$$

Steps for Completing the Square

Subtract \frac{7-6d}{d} from both sides.

$$d-\frac{7-6d}{d}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply d times \frac{d}{d}.

$$\frac{dd}{d}-\frac{7-6d}{d}=0$$

Since \frac{dd}{d} and \frac{7-6d}{d} have the same denominator, subtract them by subtracting their numerators.

$$\frac{dd-\left(7-6d\right)}{d}=0$$

Do the multiplications in dd-\left(7-6d\right).

$$\frac{d^{2}-7+6d}{d}=0$$

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d.

$$d^{2}-7+6d=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$d^{2}+6d=7$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$d^{2}+6d+3^{2}=7+3^{2}$$

Square 3.

$$d^{2}+6d+9=7+9$$

Add 7 to 9.

$$d^{2}+6d+9=16$$

Factor d^{2}+6d+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(d+3\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(d+3\right)^{2}}=\sqrt{16}$$

Simplify.

$$d+3=4 d+3=-4$$

Subtract 3 from both sides of the equation.

$$d=1 d=-7$$