How to solve ) - ) +12

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve ) - ) +12 | Equatix

Question

$$\frac { ( t ) [ 27 ( 2 - y ) - 5 ( y + 12 ) ] } { 7 - 7 y } = 8$$

Solve for t

$t=\frac{28\left(y-1\right)}{16y+3}$
$y\neq -\frac{3}{16}\text{ and }y\neq 1$

Steps for Solving Linear Equation

Multiply both sides of the equation by $7\left(-y+1\right)$.

$$t\left(27\left(2-y\right)-5\left(y+12\right)\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $27$ by $2-y$.

$$t\left(54-27y-5\left(y+12\right)\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $-5$ by $y+12$.

$$t\left(54-27y-5y-60\right)=56\left(-y+1\right)$$

Combine $-27y$ and $-5y$ to get $-32y$.

$$t\left(54-32y-60\right)=56\left(-y+1\right)$$

Subtract $60$ from $54$ to get $-6$.

$$t\left(-6-32y\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $t$ by $-6-32y$.

$$-6t-32ty=56\left(-y+1\right)$$

Use the distributive property to multiply $56$ by $-y+1$.

$$-6t-32ty=-56y+56$$

Combine all terms containing $t$.

$$\left(-6-32y\right)t=-56y+56$$

The equation is in standard form.

$$\left(-32y-6\right)t=56-56y$$

Divide both sides by $-6-32y$.

$$\frac{\left(-32y-6\right)t}{-32y-6}=\frac{56-56y}{-32y-6}$$

Dividing by $-6-32y$ undoes the multiplication by $-6-32y$.

$$t=\frac{56-56y}{-32y-6}$$

Divide $-56y+56$ by $-6-32y$.

$$t=-\frac{28\left(1-y\right)}{16y+3}$$

Show Solution

Solve for y

$y=\frac{3t+28}{4\left(7-4t\right)}$
$t\neq 0\text{ and }t\neq \frac{7}{4}$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $1$ since division by zero is not defined. Multiply both sides of the equation by $7\left(-y+1\right)$.

$$t\left(27\left(2-y\right)-5\left(y+12\right)\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $27$ by $2-y$.

$$t\left(54-27y-5\left(y+12\right)\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $-5$ by $y+12$.

$$t\left(54-27y-5y-60\right)=56\left(-y+1\right)$$

Combine $-27y$ and $-5y$ to get $-32y$.

$$t\left(54-32y-60\right)=56\left(-y+1\right)$$

Subtract $60$ from $54$ to get $-6$.

$$t\left(-6-32y\right)=56\left(-y+1\right)$$

Use the distributive property to multiply $t$ by $-6-32y$.

$$-6t-32ty=56\left(-y+1\right)$$

Use the distributive property to multiply $56$ by $-y+1$.

$$-6t-32ty=-56y+56$$

Add $56y$ to both sides.

$$-6t-32ty+56y=56$$

Add $6t$ to both sides.

$$-32ty+56y=56+6t$$

Combine all terms containing $y$.

$$\left(-32t+56\right)y=56+6t$$

The equation is in standard form.

$$\left(56-32t\right)y=6t+56$$

Divide both sides by $-32t+56$.

$$\frac{\left(56-32t\right)y}{56-32t}=\frac{6t+56}{56-32t}$$

Dividing by $-32t+56$ undoes the multiplication by $-32t+56$.

$$y=\frac{6t+56}{56-32t}$$

Divide $56+6t$ by $-32t+56$.

$$y=\frac{3t+28}{4\left(7-4t\right)}$$

Variable $y$ cannot be equal to $1$.

$$y=\frac{3t+28}{4\left(7-4t\right)}\text{, }y\neq 1$$

Show Solution

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Steps for Solving Linear Equation