Solve 4x-(2x+3)(3x-5)=49-(6x-1)(x-2)

$$4x-(2x+3)(3x-5)=49-(6x-1)(x-2)$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+3 by 3x-5 and combine like terms.

$$4x-\left(6x^{2}-x-15\right)=49-\left(6x-1\right)\left(x-2\right)$$

To find the opposite of 6x^{2}-x-15, find the opposite of each term.

$$4x-6x^{2}+x+15=49-\left(6x-1\right)\left(x-2\right)$$

Combine 4x and x to get 5x.

$$5x-6x^{2}+15=49-\left(6x-1\right)\left(x-2\right)$$

Use the distributive property to multiply 6x-1 by x-2 and combine like terms.

$$5x-6x^{2}+15=49-\left(6x^{2}-13x+2\right)$$

To find the opposite of 6x^{2}-13x+2, find the opposite of each term.

$$5x-6x^{2}+15=49-6x^{2}+13x-2$$

Subtract 2 from 49 to get 47.

$$5x-6x^{2}+15=47-6x^{2}+13x$$

Add 6x^{2} to both sides.

$$5x-6x^{2}+15+6x^{2}=47+13x$$

Combine -6x^{2} and 6x^{2} to get 0.

$$5x+15=47+13x$$

Subtract 13x from both sides.

$$5x+15-13x=47$$

Combine 5x and -13x to get -8x.

$$-8x+15=47$$

Subtract 15 from both sides.

$$-8x=47-15$$

Subtract 15 from 47 to get 32.

$$-8x=32$$

Divide both sides by -8.

$$x=\frac{32}{-8}$$

Divide 32 by -8 to get -4.

$$x=-4$$