(ax + 5)(x-b)+4x=(2x × 2x)+ cx-10equating coefficients in identities

Solve for x:
4 x + (x - b) (a x + 5) = -10 + c x + 4 x^2

Expand and collect in terms of x:
-5 b + x (9 - a b) + a x^2 = -10 + c x + 4 x^2

Subtract -10 + c x + 4 x^2 from both sides:
10 - 5 b + x (9 - a b) - c x - 4 x^2 + a x^2 = 0

Expand and collect in terms of x:
10 - 5 b + x (9 - a b - c) + x^2 (a - 4) = 0

Divide both sides by a - 4:
(10 - 5 b)/(a - 4) + (x (9 - a b - c))/(a - 4) + x^2 = 0

Subtract (10 - 5 b)/(a - 4) from both sides:
(x (9 - a b - c))/(a - 4) + x^2 = -(10 - 5 b)/(a - 4)

Add (9 - a b - c)^2/(4 (a - 4)^2) to both sides:
(9 - a b - c)^2/(4 (a - 4)^2) + (x (9 - a b - c))/(a - 4) + x^2 = (9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)

Write the left hand side as a square:
((9 - a b - c)/(2 (a - 4)) + x)^2 = (9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)

Take the square root of both sides:
(9 - a b - c)/(2 (a - 4)) + x = sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) or (9 - a b - c)/(2 (a - 4)) + x = -sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4))

Subtract (9 - a b - c)/(2 (a - 4)) from both sides:
x = sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4)) or (9 - a b - c)/(2 (a - 4)) + x = -sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4))
Subtract (9 - a b - c)/(2 (a - 4)) from both sides:
x = sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4)) or x = -sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4))