Solve for t square root of t+5t=6 square root of t

$\sqrt{t} + 5 t = 6 \sqrt{t}$

Solve for $\sqrt{t}$ .

Move all terms containing $\sqrt{t}$ to the left side of the equation.

Subtract $6 \sqrt{t}$ from both sides of the equation.

$\sqrt{t} + 5 t - 6 \sqrt{t} = 0$

Subtract $6 \sqrt{t}$ from $\sqrt{t}$ .

$- 5 \sqrt{t} + 5 t = 0$

Subtract $5 t$ from both sides of the equation.

$- 5 \sqrt{t} = - 5 t$

Divide each term in $- 5 \sqrt{t} = - 5 t$ by $- 5$ and simplify.

Divide each term in $- 5 \sqrt{t} = - 5 t$ by $- 5$ .

$\frac{- 5 \sqrt{t}}{- 5} = \frac{- 5 t}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 \sqrt{t}}{- 5} = \frac{- 5 t}{- 5}$

Divide $\sqrt{t}$ by $1$ .

$\sqrt{t} = \frac{- 5 t}{- 5}$

Simplify the right side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\sqrt{t} = \frac{- 5 t}{- 5}$

Divide $t$ by $1$ .

$\sqrt{t} = t$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{t}}^{2} = t^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{t}$ as $t^{\frac{1}{2}}$ .

${(t^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

Simplify ${(t^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(t^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$t^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$t^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

$t^{1} = t^{2}$

Simplify.

$t = t^{2}$

Solve for $t$ .

Subtract $t^{2}$ from both sides of the equation.

$t - t^{2} = 0$

Factor the left side of the equation.

Let $u = t$ . Substitute $u$ for all occurrences of $t$ .

$u - u^{2} = 0$

Factor $u$ out of $u - u^{2}$ .

Raise $u$ to the power of $1$ .

$u - u^{2} = 0$

Factor $u$ out of $u^{1}$ .

$u \cdot 1 - u^{2} = 0$

Factor $u$ out of $- u^{2}$ .

$u \cdot 1 + u (- u) = 0$

Factor $u$ out of $u \cdot 1 + u (- u)$ .

$u (1 - u) = 0$

Replace all occurrences of $u$ with $t$ .

$t (1 - t) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$t = 0$

$1 - t = 0$

Set $t$ equal to $0$ .

$t = 0$

Set $1 - t$ equal to $0$ and solve for $t$ .

Set $1 - t$ equal to $0$ .

$1 - t = 0$

Solve $1 - t = 0$ for $t$ .

Subtract $1$ from both sides of the equation.

$- t = - 1$

Divide each term in $- t = - 1$ by $- 1$ and simplify.

Divide each term in $- t = - 1$ by $- 1$ .

$\frac{- t}{- 1} = \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{- 1}{- 1}$

Divide $t$ by $1$ .

$t = \frac{- 1}{- 1}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$t = 1$

The final solution is all the values that make $t (1 - t) = 0$ true.

$t = 0, 1$

Solve for t square root of t+5t=6 square root of t

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