Solve 3x(x-3)+5(x+7)-x(x+1)-2(x^2+7)+4=0

$$3 x ( x - 3 ) + 5 ( x + 7 ) - x ( x + 1 ) - 2 ( x ^ { 2 } + 7 ) + 4 = 0$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$3x^{2}-9x+5\left(x+7\right)-x\left(x+1\right)-2\left(x^{2}+7\right)+4=0$$

Use the distributive property to multiply 5 by x+7.

$$3x^{2}-9x+5x+35-x\left(x+1\right)-2\left(x^{2}+7\right)+4=0$$

Combine -9x and 5x to get -4x.

$$3x^{2}-4x+35-x\left(x+1\right)-2\left(x^{2}+7\right)+4=0$$

Use the distributive property to multiply x by x+1.

$$3x^{2}-4x+35-\left(x^{2}+x\right)-2\left(x^{2}+7\right)+4=0$$

To find the opposite of x^{2}+x, find the opposite of each term.

$$3x^{2}-4x+35-x^{2}-x-2\left(x^{2}+7\right)+4=0$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}-4x+35-x-2\left(x^{2}+7\right)+4=0$$

Combine -4x and -x to get -5x.

$$2x^{2}-5x+35-2\left(x^{2}+7\right)+4=0$$

Use the distributive property to multiply -2 by x^{2}+7.

$$2x^{2}-5x+35-2x^{2}-14+4=0$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-5x+35-14+4=0$$

Subtract 14 from 35 to get 21.

$$-5x+21+4=0$$

Add 21 and 4 to get 25.

$$-5x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-5x=-25$$

Divide both sides by -5.

$$x=\frac{-25}{-5}$$

Divide -25 by -5 to get 5.

$$x=5$$