Solve (2x-3)^2+(3-4x)(x+5)=82

$$( 2 x - 3 ) ^ { 2 } + ( 3 - 4 x ) ( x + 5 ) = 82$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9+\left(3-4x\right)\left(x+5\right)=82$$

Use the distributive property to multiply 3-4x by x+5 and combine like terms.

$$4x^{2}-12x+9-17x+15-4x^{2}=82$$

Combine -12x and -17x to get -29x.

$$4x^{2}-29x+9+15-4x^{2}=82$$

Add 9 and 15 to get 24.

$$4x^{2}-29x+24-4x^{2}=82$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-29x+24=82$$

Subtract 24 from both sides.

$$-29x=82-24$$

Subtract 24 from 82 to get 58.

$$-29x=58$$

Divide both sides by -29.

$$x=\frac{58}{-29}$$

Divide 58 by -29 to get -2.

$$x=-2$$