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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by x-1.

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

Use the distributive property to multiply 1+x by -4.

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

To find the opposite of -4-4x, find the opposite of each term.

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

Combine -3x and 4x to get x.

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

Consider \left(1-x\right)\left(1+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To find the opposite of 1-x^{2}, find the opposite of each term.

$$3x^{2}+x+4=2x^{2}-1+x^{2}+4$$

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

$$3x^{2}+x+4=3x^{2}-1+4$$

Add -1 and 4 to get 3.

$$3x^{2}+x+4=3x^{2}+3$$

Subtract 3x^{2} from both sides.

$$3x^{2}+x+4-3x^{2}=3$$

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

$$x+4=3$$

Subtract 4 from both sides.

$$x=3-4$$

Subtract 4 from 3 to get -1.

$$x=-1$$