(ax+b)(3x+5)=24x^2-cx-30

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Solution for (ax+b)(3x+5)=24x^2-cx-30 equation: 


Simplifying
(ax + b)(3x + 5) = 24x2 + -1cx + -30

Reorder the terms:
(ax + b)(5 + 3x) = 24x2 + -1cx + -30

Multiply (ax + b) * (5 + 3x)
(ax(5 + 3x) + b(5 + 3x)) = 24x2 + -1cx + -30
((5 * ax + 3x * ax) + b(5 + 3x)) = 24x2 + -1cx + -30
((5ax + 3ax2) + b(5 + 3x)) = 24x2 + -1cx + -30
(5ax + 3ax2 + (5 * b + 3x * b)) = 24x2 + -1cx + -30
(5ax + 3ax2 + (5b + 3bx)) = 24x2 + -1cx + -30
(5ax + 3ax2 + 5b + 3bx) = 24x2 + -1cx + -30

Reorder the terms:
5ax + 3ax2 + 5b + 3bx = -30 + -1cx + 24x2

Solving
5ax + 3ax2 + 5b + 3bx = -30 + -1cx + 24x2

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5b' to each side of the equation.
5ax + 3ax2 + 5b + -5b + 3bx = -30 + -1cx + -5b + 24x2

Combine like terms: 5b + -5b = 0
5ax + 3ax2 + 0 + 3bx = -30 + -1cx + -5b + 24x2
5ax + 3ax2 + 3bx = -30 + -1cx + -5b + 24x2

Reorder the terms:
5ax + 3ax2 + 3bx = -30 + -5b + -1cx + 24x2

Add '-3bx' to each side of the equation.
5ax + 3ax2 + 3bx + -3bx = -30 + -5b + -1cx + -3bx + 24x2

Combine like terms: 3bx + -3bx = 0
5ax + 3ax2 + 0 = -30 + -5b + -1cx + -3bx + 24x2
5ax + 3ax2 = -30 + -5b + -1cx + -3bx + 24x2

Reorder the terms:
5ax + 3ax2 = -30 + -5b + -3bx + -1cx + 24x2

Reorder the terms:
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = -30 + -5b + -3bx + -1cx + 24x2 + 30 + 5b + 3bx + cx + -24x2

Reorder the terms:
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = -30 + 30 + -5b + 5b + -3bx + 3bx + -1cx + cx + 24x2 + -24x2

Combine like terms: -30 + 30 = 0
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 0 + -5b + 5b + -3bx + 3bx + -1cx + cx + 24x2 + -24x2
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = -5b + 5b + -3bx + 3bx + -1cx + cx + 24x2 + -24x2

Combine like terms: -5b + 5b = 0
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 0 + -3bx + 3bx + -1cx + cx + 24x2 + -24x2
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = -3bx + 3bx + -1cx + cx + 24x2 + -24x2

Combine like terms: -3bx + 3bx = 0
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 0 + -1cx + cx + 24x2 + -24x2
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = -1cx + cx + 24x2 + -24x2

Combine like terms: -1cx + cx = 0
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 0 + 24x2 + -24x2
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
30 + 5ax + 3ax2 + 5b + 3bx + cx + -24x2 = 0

The solution to this equation could not be determined.

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