Solve for t 4(9+3t)-12=-6

$4 (9 + 3 t) - 12 = - 6$

Step 1

Simplify $4 (9 + 3 t) - 12$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 9 + 4 (3 t) - 12 = - 6$

Multiply $4$ by $9$ .

$36 + 4 (3 t) - 12 = - 6$

Multiply $3$ by $4$ .

$36 + 12 t - 12 = - 6$

Subtract $12$ from $36$ .

$12 t + 24 = - 6$

Step 2

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

Subtract $24$ from both sides of the equation.

$12 t = - 6 - 24$

Subtract $24$ from $- 6$ .

$12 t = - 30$

Step 3

Divide each term in $12 t = - 30$ by $12$ and simplify.

Divide each term in $12 t = - 30$ by $12$ .

$\frac{12 t}{12} = \frac{- 30}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 t}{12} = \frac{- 30}{12}$

Divide $t$ by $1$ .

$t = \frac{- 30}{12}$

Simplify the right side.

Cancel the common factor of $- 30$ and $12$ .

Factor $6$ out of $- 30$ .

$t = \frac{6 (- 5)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$t = \frac{6 \cdot - 5}{6 \cdot 2}$

Cancel the common factor.

$t = \frac{6 \cdot - 5}{6 \cdot 2}$

Rewrite the expression.

$t = \frac{- 5}{2}$

Move the negative in front of the fraction.

$t = - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{5}{2}$

Decimal Form:

$t = - 2.5$

Mixed Number Form:

$t = - 2 \frac{1}{2}$

Solve for t 4(9+3t)-12=-6

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