Solve 15(x-9)-2(x-12)+5(x+6)=0

$$15 ( x - 9 ) - 2 ( x - 12 ) + 5 ( x + 6 ) = 0$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 15 by x-9.

$$15x-135-2\left(x-12\right)+5\left(x+6\right)=0$$

Use the distributive property to multiply -2 by x-12.

$$15x-135-2x+24+5\left(x+6\right)=0$$

Combine 15x and -2x to get 13x.

$$13x-135+24+5\left(x+6\right)=0$$

Add -135 and 24 to get -111.

$$13x-111+5\left(x+6\right)=0$$

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

$$13x-111+5x+30=0$$

Combine 13x and 5x to get 18x.

$$18x-111+30=0$$

Add -111 and 30 to get -81.

$$18x-81=0$$

Add 81 to both sides. Anything plus zero gives itself.

$$18x=81$$

Divide both sides by 18.

$$x=\frac{81}{18}$$

Reduce the fraction \frac{81}{18} to lowest terms by extracting and canceling out 9.

$$x=\frac{9}{2}$$