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

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

Solve for x

$$x=-\frac{3}{10}=-0.3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by 3x-4.

$$3+6x^{2}-8x=4x\left(2x-5\right)-2x\left(x-1\right)$$

Use the distributive property to multiply 4x by 2x-5.

$$3+6x^{2}-8x=8x^{2}-20x-2x\left(x-1\right)$$

Add 2x\left(x-1\right) to both sides.

$$3+6x^{2}-8x+2x\left(x-1\right)=8x^{2}-20x$$

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

$$3+6x^{2}-8x+2x^{2}-2x=8x^{2}-20x$$

Combine 6x^{2} and 2x^{2} to get 8x^{2}.

$$3+8x^{2}-8x-2x=8x^{2}-20x$$

Combine -8x and -2x to get -10x.

$$3+8x^{2}-10x=8x^{2}-20x$$

Subtract 8x^{2} from both sides.

$$3+8x^{2}-10x-8x^{2}=-20x$$

Combine 8x^{2} and -8x^{2} to get 0.

$$3-10x=-20x$$

Add 20x to both sides.

$$3-10x+20x=0$$

Combine -10x and 20x to get 10x.

$$3+10x=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$10x=-3$$

Divide both sides by 10.

$$x=\frac{-3}{10}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$x=-\frac{3}{10}$$