Solve 5(2x+6)(2x-6)+4(3x-1)^2=(7x-10)(8x+33)=

$$5 ( 2 x + 6 ) ( 2 x - 6 ) + 4 ( 3 x - 1 ) ^ { 2 } = ( 7 x - 10 ) ( 8 x + 33 ) =$$

Solve for x

$$x=\frac{22}{25}=0.88$$

Steps for Solving Linear Equation

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

$$\left(10x+30\right)\left(2x-6\right)+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+33\right)$$

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

$$20x^{2}-180+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+33\right)$$

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

$$20x^{2}-180+4\left(9x^{2}-6x+1\right)=\left(7x-10\right)\left(8x+33\right)$$

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

$$20x^{2}-180+36x^{2}-24x+4=\left(7x-10\right)\left(8x+33\right)$$

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

$$56x^{2}-180-24x+4=\left(7x-10\right)\left(8x+33\right)$$

Add -180 and 4 to get -176.

$$56x^{2}-176-24x=\left(7x-10\right)\left(8x+33\right)$$

Use the distributive property to multiply 7x-10 by 8x+33 and combine like terms.

$$56x^{2}-176-24x=56x^{2}+151x-330$$

Subtract 56x^{2} from both sides.

$$56x^{2}-176-24x-56x^{2}=151x-330$$

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

$$-176-24x=151x-330$$

Subtract 151x from both sides.

$$-176-24x-151x=-330$$

Combine -24x and -151x to get -175x.

$$-176-175x=-330$$

Add 176 to both sides.

$$-175x=-330+176$$

Add -330 and 176 to get -154.

$$-175x=-154$$

Divide both sides by -175.

$$x=\frac{-154}{-175}$$

Reduce the fraction \frac{-154}{-175} to lowest terms by extracting and canceling out -7.

$$x=\frac{22}{25}$$