6x^2+5x-21=(2x-3)(ax+b)

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Solution for 6x^2+5x-21=(2x-3)(ax+b) equation: 


Simplifying
6x2 + 5x + -21 = (2x + -3)(ax + b)

Reorder the terms:
-21 + 5x + 6x2 = (2x + -3)(ax + b)

Reorder the terms:
-21 + 5x + 6x2 = (-3 + 2x)(ax + b)

Multiply (-3 + 2x) * (ax + b)
-21 + 5x + 6x2 = (-3(ax + b) + 2x * (ax + b))
-21 + 5x + 6x2 = ((ax * -3 + b * -3) + 2x * (ax + b))
-21 + 5x + 6x2 = ((-3ax + -3b) + 2x * (ax + b))
-21 + 5x + 6x2 = (-3ax + -3b + (ax * 2x + b * 2x))
-21 + 5x + 6x2 = (-3ax + -3b + (2ax2 + 2bx))

Reorder the terms:
-21 + 5x + 6x2 = (-3ax + 2ax2 + -3b + 2bx)
-21 + 5x + 6x2 = (-3ax + 2ax2 + -3b + 2bx)

Solving
-21 + 5x + 6x2 = -3ax + 2ax2 + -3b + 2bx

Solving for variable 'x'.

Reorder the terms:
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = -3ax + 2ax2 + -3b + 2bx + 3ax + -2ax2 + 3b + -2bx

Reorder the terms:
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = -3ax + 3ax + 2ax2 + -2ax2 + -3b + 3b + 2bx + -2bx

Combine like terms: -3ax + 3ax = 0
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 0 + 2ax2 + -2ax2 + -3b + 3b + 2bx + -2bx
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 2ax2 + -2ax2 + -3b + 3b + 2bx + -2bx

Combine like terms: 2ax2 + -2ax2 = 0
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 0 + -3b + 3b + 2bx + -2bx
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = -3b + 3b + 2bx + -2bx

Combine like terms: -3b + 3b = 0
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 0 + 2bx + -2bx
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 2bx + -2bx

Combine like terms: 2bx + -2bx = 0
-21 + 3ax + -2ax2 + 3b + -2bx + 5x + 6x2 = 0

The solution to this equation could not be determined.

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