Solve 5left(2x+6right)left(2x-6right)+4left(3x-1right)^2=left(7x-10right)left(8x+3right)-6

$$5 \left( 2x+6 \right) \left( 2x-6 \right) +4 { \left(3x-1 \right) }^{ 2 } = \left( 7x-10 \right) \left( 8x+3 \right) -6$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2x+6.

$$\left(10x+30\right)\left(2x-6\right)+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+3\right)-6$$

Use the distributive property to multiply 10x+30 by 2x-6 and combine like terms.

$$20x^{2}-180+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+3\right)-6$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-1\right)^{2}.

$$20x^{2}-180+4\left(9x^{2}-6x+1\right)=\left(7x-10\right)\left(8x+3\right)-6$$

Use the distributive property to multiply 4 by 9x^{2}-6x+1.

$$20x^{2}-180+36x^{2}-24x+4=\left(7x-10\right)\left(8x+3\right)-6$$

Combine 20x^{2} and 36x^{2} to get 56x^{2}.

$$56x^{2}-180-24x+4=\left(7x-10\right)\left(8x+3\right)-6$$

Add -180 and 4 to get -176.

$$56x^{2}-176-24x=\left(7x-10\right)\left(8x+3\right)-6$$

Use the distributive property to multiply 7x-10 by 8x+3 and combine like terms.

$$56x^{2}-176-24x=56x^{2}-59x-30-6$$

Subtract 6 from -30 to get -36.

$$56x^{2}-176-24x=56x^{2}-59x-36$$

Subtract 56x^{2} from both sides.

$$56x^{2}-176-24x-56x^{2}=-59x-36$$

Combine 56x^{2} and -56x^{2} to get 0.

$$-176-24x=-59x-36$$

Add 59x to both sides.

$$-176-24x+59x=-36$$

Combine -24x and 59x to get 35x.

$$-176+35x=-36$$

Add 176 to both sides.

$$35x=-36+176$$

Add -36 and 176 to get 140.

$$35x=140$$

Divide both sides by 35.

$$x=\frac{140}{35}$$

Divide 140 by 35 to get 4.

$$x=4$$