Solve for y (3y-9)^2+7=43

${(3 y - 9)}^{2} + 7 = 43$

Step 1

Subtract $7$ from both sides of the equation.

${(3 y - 9)}^{2} = 43 - 7$

Step 2

Subtract $7$ from $43$ .

${(3 y - 9)}^{2} = 36$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$3 y - 9 = \pm \sqrt{36}$

Step 4

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$3 y - 9 = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$3 y - 9 = \pm 6$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$3 y - 9 = 6$

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

Add $9$ to both sides of the equation.

$3 y = 6 + 9$

Add $6$ and $9$ .

$3 y = 15$

Divide each term in $3 y = 15$ by $3$ and simplify.

Divide each term in $3 y = 15$ by $3$ .

$\frac{3 y}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{15}{3}$

Divide $y$ by $1$ .

$y = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$y = 5$

Next, use the negative value of the $\pm$ to find the second solution.

$3 y - 9 = - 6$

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

Add $9$ to both sides of the equation.

$3 y = - 6 + 9$

Add $- 6$ and $9$ .

$3 y = 3$

Divide each term in $3 y = 3$ by $3$ and simplify.

Divide each term in $3 y = 3$ by $3$ .

$\frac{3 y}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{3}{3}$

Divide $y$ by $1$ .

$y = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$y = 1$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 5, 1$

Solve for y (3y-9)^2+7=43

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