Solve for t 7(t^2+5t-9)+t=t(7t-2)+13

$7 (t^{2} + 5 t - 9) + t = t (7 t - 2) + 13$

Step 1

Simplify $7 (t^{2} + 5 t - 9) + t$ .

Simplify each term.

Apply the distributive property.

$7 t^{2} + 7 (5 t) + 7 \cdot - 9 + t = t (7 t - 2) + 13$

Simplify.

Multiply $5$ by $7$ .

$7 t^{2} + 35 t + 7 \cdot - 9 + t = t (7 t - 2) + 13$

Multiply $7$ by $- 9$ .

$7 t^{2} + 35 t - 63 + t = t (7 t - 2) + 13$

Add $35 t$ and $t$ .

$7 t^{2} + 36 t - 63 = t (7 t - 2) + 13$

Step 2

Simplify each term.

Apply the distributive property.

$7 t^{2} + 36 t - 63 = t (7 t) + t \cdot - 2 + 13$

Rewrite using the commutative property of multiplication.

$7 t^{2} + 36 t - 63 = 7 t \cdot t + t \cdot - 2 + 13$

Move $- 2$ to the left of $t$ .

$7 t^{2} + 36 t - 63 = 7 t \cdot t - 2 \cdot t + 13$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$7 t^{2} + 36 t - 63 = 7 (t \cdot t) - 2 \cdot t + 13$

Multiply $t$ by $t$ .

$7 t^{2} + 36 t - 63 = 7 t^{2} - 2 \cdot t + 13$

$7 t^{2} + 36 t - 63 = 7 t^{2} - 2 t + 13$

Step 3

Move all terms containing $t$ to the left side of the equation.

Subtract $7 t^{2}$ from both sides of the equation.

$7 t^{2} + 36 t - 63 - 7 t^{2} = - 2 t + 13$

Add $2 t$ to both sides of the equation.

$7 t^{2} + 36 t - 63 - 7 t^{2} + 2 t = 13$

Combine the opposite terms in $7 t^{2} + 36 t - 63 - 7 t^{2} + 2 t$ .

Subtract $7 t^{2}$ from $7 t^{2}$ .

$36 t - 63 + 0 + 2 t = 13$

Add $36 t - 63$ and $0$ .

$36 t - 63 + 2 t = 13$

Add $36 t$ and $2 t$ .

$38 t - 63 = 13$

Step 4

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

Add $63$ to both sides of the equation.

$38 t = 13 + 63$

Add $13$ and $63$ .

$38 t = 76$

Step 5

Divide each term in $38 t = 76$ by $38$ and simplify.

Divide each term in $38 t = 76$ by $38$ .

$\frac{38 t}{38} = \frac{76}{38}$

Simplify the left side.

Cancel the common factor of $38$ .

Cancel the common factor.

$\frac{38 t}{38} = \frac{76}{38}$

Divide $t$ by $1$ .

$t = \frac{76}{38}$

Simplify the right side.

Divide $76$ by $38$ .

$t = 2$

Solve for t 7(t^2+5t-9)+t=t(7t-2)+13

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