Solve -5left(3x-6right)+4left(-5y-7right)=0

$$-5 \left( 3x-6 \right) +4 \left( -5y-7 \right) = 0$$

Solve for x

$$x=-\frac{4y}{3}+\frac{2}{15}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by 3x-6.

$$-15x+30+4\left(-5y-7\right)=0$$

Use the distributive property to multiply 4 by -5y-7.

$$-15x+30-20y-28=0$$

Subtract 28 from 30 to get 2.

$$-15x+2-20y=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-15x-20y=-2$$

Add 20y to both sides.

$$-15x=-2+20y$$

The equation is in standard form.

$$-15x=20y-2$$

Divide both sides by -15.

$$\frac{-15x}{-15}=\frac{20y-2}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x=\frac{20y-2}{-15}$$

Divide -2+20y by -15.

$$x=-\frac{4y}{3}+\frac{2}{15}$$

Solve for y

$$y=-\frac{3x}{4}+\frac{1}{10}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by 3x-6.

$$-15x+30+4\left(-5y-7\right)=0$$

Use the distributive property to multiply 4 by -5y-7.

$$-15x+30-20y-28=0$$

Subtract 28 from 30 to get 2.

$$-15x+2-20y=0$$

Add 15x to both sides. Anything plus zero gives itself.

$$2-20y=15x$$

Subtract 2 from both sides.

$$-20y=15x-2$$

Divide both sides by -20.

$$\frac{-20y}{-20}=\frac{15x-2}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$y=\frac{15x-2}{-20}$$

Divide 15x-2 by -20.

$$y=-\frac{3x}{4}+\frac{1}{10}$$