To expand the left side of the equation, we will use the FOIL method:
(5x + 3)(4 - x)= 5x(4) + 5x(-x) + 3(4) + 3(-x)= 20x - 5x^2 + 12 - 3x= -5x^2 + 17x + 12
Setting this expression equal to x^2 - 7, we get:
-5x^2 + 17x + 12 = x^2 - 7
Rearranging the terms to the standard form ax^2 + bx + c = 0:
-5x^2 - x^2 + 17x - 12 + 7 = 0-6x^2 + 17x - 5 = 0
Therefore, the equation in the desired form is -6x^2 + 17x - 5 = 0.
To expand the left side of the equation, we will use the FOIL method:
(5x + 3)(4 - x)
= 5x(4) + 5x(-x) + 3(4) + 3(-x)
= 20x - 5x^2 + 12 - 3x
= -5x^2 + 17x + 12
Setting this expression equal to x^2 - 7, we get:
-5x^2 + 17x + 12 = x^2 - 7
Rearranging the terms to the standard form ax^2 + bx + c = 0:
-5x^2 - x^2 + 17x - 12 + 7 = 0
-6x^2 + 17x - 5 = 0
Therefore, the equation in the desired form is -6x^2 + 17x - 5 = 0.