Answer:
[tex]c=\dfrac{-(4g+25)}{g+6}[/tex]
Step-by-step explanation:
Given equation:
[tex]g=\dfrac{c+3}{4+c}-7[/tex]
To make c the subject of the given equation, begin by adding 7 to both sides:
[tex]g+7=\dfrac{c+3}{4+c}[/tex]
Multiply both sides by (4 + c):
[tex](g+7)(4+c)=c+3[/tex]
Expand the left side:
[tex]4g+cg+28+7c=c+3[/tex]
Rearrange the equation so the terms in c are on the left side and the other terms are on the right side:
[tex]cg+7c-c=3-28-4g[/tex]
[tex]cg+6c=-4g-25[/tex]
Factor out c from the left side and factor out negative 1 from the right side:
[tex]c(g+6)=-(4g+25)[/tex]
Divide both sides by (g + 6):
[tex]c=\dfrac{-(4g+25)}{g+6}[/tex]