(3x+a)(x+b)=3x^2+7x+k

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Solution for (3x+a)(x+b)=3x^2+7x+k equation: 


Simplifying
(3x + a)(x + b) = 3x2 + 7x + k

Reorder the terms:
(a + 3x)(x + b) = 3x2 + 7x + k

Reorder the terms:
(a + 3x)(b + x) = 3x2 + 7x + k

Multiply (a + 3x) * (b + x)
(a(b + x) + 3x * (b + x)) = 3x2 + 7x + k
((b * a + x * a) + 3x * (b + x)) = 3x2 + 7x + k
((ab + ax) + 3x * (b + x)) = 3x2 + 7x + k
(ab + ax + (b * 3x + x * 3x)) = 3x2 + 7x + k
(ab + ax + (3bx + 3x2)) = 3x2 + 7x + k
(ab + ax + 3bx + 3x2) = 3x2 + 7x + k

Reorder the terms:
ab + ax + 3bx + 3x2 = k + 7x + 3x2

Add '-3x2' to each side of the equation.
ab + ax + 3bx + 3x2 + -3x2 = k + 7x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
ab + ax + 3bx + 0 = k + 7x + 3x2 + -3x2
ab + ax + 3bx = k + 7x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
ab + ax + 3bx = k + 7x + 0
ab + ax + 3bx = k + 7x

Solving
ab + ax + 3bx = k + 7x

Solving for variable 'a'.

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

Add '-3bx' to each side of the equation.
ab + ax + 3bx + -3bx = k + -3bx + 7x

Combine like terms: 3bx + -3bx = 0
ab + ax + 0 = k + -3bx + 7x
ab + ax = k + -3bx + 7x

Reorder the terms:
ab + ax = -3bx + k + 7x

Reorder the terms:
ab + ax + 3bx + -1k + -7x = -3bx + 3bx + k + -1k + 7x + -7x

Combine like terms: -3bx + 3bx = 0
ab + ax + 3bx + -1k + -7x = 0 + k + -1k + 7x + -7x
ab + ax + 3bx + -1k + -7x = k + -1k + 7x + -7x

Combine like terms: k + -1k = 0
ab + ax + 3bx + -1k + -7x = 0 + 7x + -7x
ab + ax + 3bx + -1k + -7x = 7x + -7x

Combine like terms: 7x + -7x = 0
ab + ax + 3bx + -1k + -7x = 0

The solution to this equation could not be determined.

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