The value of g should be equal to 3, to make the equation true.
Given data:
The equation is, [tex](x+7)(x-4)=x^{2}+gx-28[/tex].
The given equation is a quadratic equation with an unknown variable g at right hand side (RHS).
To obtain the value of unknown variable, solve the left hand side (LHS) of the given equation as,
[tex](x+7)(x-4)=x^{2}+gx-28\\x^{2}-4x+7x-28=x^{2}+gx-28[/tex]
[tex]x^{2}+3x-28=x^{2}+gx-28 ....................................................(1)[/tex]
Now, compare the coefficients of each variable from left hand side and right hand side of equation (1) to obtain,
[tex]x^{2}+3x-28=x^{2}+gx-28\\ \\3= g[/tex]
Thus, we can conclude that the value of g should be equal to 3, to make the equation true.
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