Solve 5(x-4)-2(x-9)+5(x+6)=0

$$5(x-4)-2(x-9)+5(x+6)=0$$

Solve for x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-4.

$$5x-20-2\left(x-9\right)+5\left(x+6\right)=0$$

Use the distributive property to multiply -2 by x-9.

$$5x-20-2x+18+5\left(x+6\right)=0$$

Combine 5x and -2x to get 3x.

$$3x-20+18+5\left(x+6\right)=0$$

Add -20 and 18 to get -2.

$$3x-2+5\left(x+6\right)=0$$

Use the distributive property to multiply 5 by x+6.

$$3x-2+5x+30=0$$

Combine 3x and 5x to get 8x.

$$8x-2+30=0$$

Add -2 and 30 to get 28.

$$8x+28=0$$

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

$$8x=-28$$

Divide both sides by 8.

$$x=\frac{-28}{8}$$

Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{7}{2}$$