Solve x(3x-4)+2x(x+1)=5x(x-7)+90

$$x ( 3 x - 4 ) + 2 x ( x + 1 ) = 5 x ( x - 7 ) + 90$$

Solve for x

$$x = \frac{30}{11} = 2\frac{8}{11} \approx 2.727272727$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3x-4.

$$3x^{2}-4x+2x\left(x+1\right)=5x\left(x-7\right)+90$$

Use the distributive property to multiply 2x by x+1.

$$3x^{2}-4x+2x^{2}+2x=5x\left(x-7\right)+90$$

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

$$5x^{2}-4x+2x=5x\left(x-7\right)+90$$

Combine -4x and 2x to get -2x.

$$5x^{2}-2x=5x\left(x-7\right)+90$$

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

$$5x^{2}-2x=5x^{2}-35x+90$$

Subtract 5x^{2} from both sides.

$$5x^{2}-2x-5x^{2}=-35x+90$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-2x=-35x+90$$

Add 35x to both sides.

$$-2x+35x=90$$

Combine -2x and 35x to get 33x.

$$33x=90$$

Divide both sides by 33.

$$x=\frac{90}{33}$$

Reduce the fraction \frac{90}{33} to lowest terms by extracting and canceling out 3.

$$x=\frac{30}{11}$$