(px-7)(2x+q)=12x^2+16x+r

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Solution for (px-7)(2x+q)=12x^2+16x+r equation: 


Simplifying
(px + -7)(2x + q) = 12x2 + 16x + r

Reorder the terms:
(-7 + px)(2x + q) = 12x2 + 16x + r

Reorder the terms:
(-7 + px)(q + 2x) = 12x2 + 16x + r

Multiply (-7 + px) * (q + 2x)
(-7(q + 2x) + px(q + 2x)) = 12x2 + 16x + r
((q * -7 + 2x * -7) + px(q + 2x)) = 12x2 + 16x + r
((-7q + -14x) + px(q + 2x)) = 12x2 + 16x + r
(-7q + -14x + (q * px + 2x * px)) = 12x2 + 16x + r
(-7q + -14x + (pqx + 2px2)) = 12x2 + 16x + r

Reorder the terms:
(pqx + 2px2 + -7q + -14x) = 12x2 + 16x + r
(pqx + 2px2 + -7q + -14x) = 12x2 + 16x + r

Reorder the terms:
pqx + 2px2 + -7q + -14x = r + 16x + 12x2

Solving
pqx + 2px2 + -7q + -14x = r + 16x + 12x2

Solving for variable 'p'.

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

Add '7q' to each side of the equation.
pqx + 2px2 + -7q + 7q + -14x = r + 16x + 7q + 12x2

Combine like terms: -7q + 7q = 0
pqx + 2px2 + 0 + -14x = r + 16x + 7q + 12x2
pqx + 2px2 + -14x = r + 16x + 7q + 12x2

Reorder the terms:
pqx + 2px2 + -14x = 7q + r + 16x + 12x2

Add '14x' to each side of the equation.
pqx + 2px2 + -14x + 14x = 7q + r + 16x + 14x + 12x2

Combine like terms: -14x + 14x = 0
pqx + 2px2 + 0 = 7q + r + 16x + 14x + 12x2
pqx + 2px2 = 7q + r + 16x + 14x + 12x2

Combine like terms: 16x + 14x = 30x
pqx + 2px2 = 7q + r + 30x + 12x2

Reorder the terms:
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 7q + -7q + r + -1r + 30x + -30x + 12x2 + -12x2

Combine like terms: 7q + -7q = 0
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 0 + r + -1r + 30x + -30x + 12x2 + -12x2
pqx + 2px2 + -7q + -1r + -30x + -12x2 = r + -1r + 30x + -30x + 12x2 + -12x2

Combine like terms: r + -1r = 0
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 0 + 30x + -30x + 12x2 + -12x2
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 30x + -30x + 12x2 + -12x2

Combine like terms: 30x + -30x = 0
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 0 + 12x2 + -12x2
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
pqx + 2px2 + -7q + -1r + -30x + -12x2 = 0

The solution to this equation could not be determined.

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