Solve (5x-1)^2-(1-3x)^2=16x(x-3)

$$( 5 x - 1 ) ^ { 2 } - ( 1 - 3 x ) ^ { 2 } = 16 x ( x - 3 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x-1\right)^{2}.

$$25x^{2}-10x+1-\left(1-3x\right)^{2}=16x\left(x-3\right)$$

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

$$25x^{2}-10x+1-\left(1-6x+9x^{2}\right)=16x\left(x-3\right)$$

To find the opposite of 1-6x+9x^{2}, find the opposite of each term.

$$25x^{2}-10x+1-1+6x-9x^{2}=16x\left(x-3\right)$$

Subtract 1 from 1 to get 0.

$$25x^{2}-10x+6x-9x^{2}=16x\left(x-3\right)$$

Combine -10x and 6x to get -4x.

$$25x^{2}-4x-9x^{2}=16x\left(x-3\right)$$

Combine 25x^{2} and -9x^{2} to get 16x^{2}.

$$16x^{2}-4x=16x\left(x-3\right)$$

Use the distributive property to multiply 16x by x-3.

$$16x^{2}-4x=16x^{2}-48x$$

Subtract 16x^{2} from both sides.

$$16x^{2}-4x-16x^{2}=-48x$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-4x=-48x$$

Add 48x to both sides.

$$-4x+48x=0$$

Combine -4x and 48x to get 44x.

$$44x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 44 is not equal to 0, x must be equal to 0.

$$x=0$$