6x^2+14x+4=(ax+b)(cx+d)

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Solution for 6x^2+14x+4=(ax+b)(cx+d) equation: 


Simplifying
6x2 + 14x + 4 = (ax + b)(cx + d)

Reorder the terms:
4 + 14x + 6x2 = (ax + b)(cx + d)

Multiply (ax + b) * (cx + d)
4 + 14x + 6x2 = (ax(cx + d) + b(cx + d))
4 + 14x + 6x2 = ((cx * ax + d * ax) + b(cx + d))
4 + 14x + 6x2 = ((acx2 + adx) + b(cx + d))
4 + 14x + 6x2 = (acx2 + adx + (cx * b + d * b))
4 + 14x + 6x2 = (acx2 + adx + (bcx + bd))
4 + 14x + 6x2 = (acx2 + adx + bcx + bd)

Solving
4 + 14x + 6x2 = acx2 + adx + bcx + bd

Solving for variable 'x'.

Reorder the terms:
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = acx2 + adx + bcx + bd + -1acx2 + -1adx + -1bcx + -1bd

Reorder the terms:
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = acx2 + -1acx2 + adx + -1adx + bcx + -1bcx + bd + -1bd

Combine like terms: acx2 + -1acx2 = 0
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = 0 + adx + -1adx + bcx + -1bcx + bd + -1bd
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = adx + -1adx + bcx + -1bcx + bd + -1bd

Combine like terms: adx + -1adx = 0
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = 0 + bcx + -1bcx + bd + -1bd
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = bcx + -1bcx + bd + -1bd

Combine like terms: bcx + -1bcx = 0
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = 0 + bd + -1bd
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = bd + -1bd

Combine like terms: bd + -1bd = 0
4 + -1acx2 + -1adx + -1bcx + -1bd + 14x + 6x2 = 0

The solution to this equation could not be determined.

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