a: \(\left(4x+1\right)^2-\left(4x+5\right)\left(4x-5\right)=2x+3\)
=>\(16x^2+8x+1-\left(16x^2-25\right)=2x+3\)
=>\(16x^2+8x+1-16x^2+25=2x+3\)
=>8x+26=2x+3
=>6x=-23
=>\(x=-\dfrac{23}{6}\)
b: \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x+1\right)^2=5x\)
=>\(x^3+3^3-x\left(x^2+2x+1\right)=5x\)
=>\(x^3+27-x^3-2x^2-x-5x=0\)
=>\(-2x^2-6x+27=0\)
=>\(x=\dfrac{-3\pm3\sqrt{7}}{2}\)
c: \(\left(2x-1\right)\left(2x+1\right)-4\left(x+6\right)^2=3\left(x-4\right)\)
=>\(4x^2-1-4\left(x^2+12x+36\right)=3x-12\)
=>\(4x^2-1-4x^2-48x-144-3x+12=0\)
=>-51x-133=0
=>51x=-133
=>\(x=-\dfrac{133}{51}\)
`a)(4x+1)^2-(4x+5)(4x-5)=2x+3`
`<=>(4x)^2+2.4x+1-(4x)^2+25=2x+3`
`<=>16x^2+8x+1-16x^2+25=2x+3`
`<=>6x+26=3`
`<=>6x=-23`
`<=>x=-23/6`
`b)(x+3)(x^2-3x+9)-x(x+1)^2=5x`
`<=>x^3+27-(x^3+2x^2+x)=5x`
`<=>27-2x^2-x=5x`
`<=>2x^2+6x-27=0`
`<=>x=(-3+-3\sqrt7)/2`
`c)(2x-1)(2x+1)-4(x+6)^2=3(x-4)`
`<=>4x^2-1-4(x^2+12x+36)=3x-12`
`<=>-48x-145=3x-12`
`<=>51x=133`
`<=>x=-133/51`
\(a.\left(4x+1\right)^2-\left(4x+5\right)\left(4x-5\right)=2x+3\\ \Leftrightarrow\left(16x^2+8x+1\right)-\left(16x^2-25\right)=2x+3\\ \Leftrightarrow16x^2+8x+1-16x^2+25=2x+3\\ \Leftrightarrow8x+26=2x+3\\ \Leftrightarrow8x-2x=3-26\\ \Leftrightarrow6x=-23\\ \Leftrightarrow x=-\dfrac{23}{6}\\ b.\left(x+3\right)\left(x^2-3x+9\right)-x\left(x+1\right)^2=5x\\ \Leftrightarrow\left(x^3+3^3\right)-x\left(x^2+2x+1\right)=5x\\ \Leftrightarrow x^3+27-x^3-2x^2-x=5x\\ \Leftrightarrow27-2x^2-x=5x\\ \Leftrightarrow2x^2+5x+x-27=0\\ \Leftrightarrow2x^2+6x-27=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3\sqrt{7}-3}{2}\\x=\dfrac{-3\sqrt{7}-3}{2}\end{matrix}\right.\\ c.\left(2x-1\right)\left(2x+1\right)-4\left(x+6\right)^2=3\left(x-4\right)\\ \Leftrightarrow\left(4x^2-1\right)-4\left(x^2+12x+36\right)=3x-12\\ \Leftrightarrow4x^2-1-4x^2-48x-144=3x-12\\ \Leftrightarrow-48x-145=3x-12\\ \Leftrightarrow3x+48x=-145+12\\ \Leftrightarrow51x=-133\\ \Leftrightarrow x=-\dfrac{133}{51}\)
