Solve (4x-1)^2-(4x-7)*(4x+1)+28=-10

$$( 4 x - 1 ) ^ { 2 } - ( 4 x - 7 ) \cdot ( 4 x + 1 ) + 28 = - 10$$

Solve for x

$$x = -\frac{23}{8} = -2\frac{7}{8} = -2.875$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}-8x+1-\left(4x-7\right)\left(4x+1\right)+28=-10$$

Use the distributive property to multiply 4x-7 by 4x+1 and combine like terms.

$$16x^{2}-8x+1-\left(16x^{2}-24x-7\right)+28=-10$$

To find the opposite of 16x^{2}-24x-7, find the opposite of each term.

$$16x^{2}-8x+1-16x^{2}+24x+7+28=-10$$

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

$$-8x+1+24x+7+28=-10$$

Combine -8x and 24x to get 16x.

$$16x+1+7+28=-10$$

Add 1 and 7 to get 8.

$$16x+8+28=-10$$

Add 8 and 28 to get 36.

$$16x+36=-10$$

Subtract 36 from both sides.

$$16x=-10-36$$

Subtract 36 from -10 to get -46.

$$16x=-46$$

Divide both sides by 16.

$$x=\frac{-46}{16}$$

Reduce the fraction \frac{-46}{16} to lowest terms by extracting and canceling out 2.

$$x=-\frac{23}{8}$$