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

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

Solve for x

$$x = -\frac{21}{11} = -1\frac{10}{11} \approx -1.909090909$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x+7 by x-3 and combine like terms.

$$4x^{2}-5x-21-x^{2}=3x\left(x+2\right)$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-5x-21=3x\left(x+2\right)$$

Use the distributive property to multiply 3x by x+2.

$$3x^{2}-5x-21=3x^{2}+6x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-5x-21-3x^{2}=6x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-5x-21=6x$$

Subtract 6x from both sides.

$$-5x-21-6x=0$$

Combine -5x and -6x to get -11x.

$$-11x-21=0$$

Add 21 to both sides. Anything plus zero gives itself.

$$-11x=21$$

Divide both sides by -11.

$$x=\frac{21}{-11}$$

Fraction \frac{21}{-11} can be rewritten as -\frac{21}{11} by extracting the negative sign.

$$x=-\frac{21}{11}$$