(x^2+5x-14)=(x+a)(x-b)

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Solution for (x^2+5x-14)=(x+a)(x-b) equation:


Simplifying
(x2 + 5x + -14) = (x + a)(x + -1b)

Reorder the terms:
(-14 + 5x + x2) = (x + a)(x + -1b)

Remove parenthesis around (-14 + 5x + x2)
-14 + 5x + x2 = (x + a)(x + -1b)

Reorder the terms:
-14 + 5x + x2 = (a + x)(x + -1b)

Reorder the terms:
-14 + 5x + x2 = (a + x)(-1b + x)

Multiply (a + x) * (-1b + x)
-14 + 5x + x2 = (a(-1b + x) + x(-1b + x))
-14 + 5x + x2 = ((-1b * a + x * a) + x(-1b + x))
-14 + 5x + x2 = ((-1ab + ax) + x(-1b + x))
-14 + 5x + x2 = (-1ab + ax + (-1b * x + x * x))
-14 + 5x + x2 = (-1ab + ax + (-1bx + x2))
-14 + 5x + x2 = (-1ab + ax + -1bx + x2)

Add '-1x2' to each side of the equation.
-14 + 5x + x2 + -1x2 = -1ab + ax + -1bx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 5x + 0 = -1ab + ax + -1bx + x2 + -1x2
-14 + 5x = -1ab + ax + -1bx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 5x = -1ab + ax + -1bx + 0
-14 + 5x = -1ab + ax + -1bx

Solving
-14 + 5x = -1ab + ax + -1bx

Solving for variable 'x'.

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

Add '-1ax' to each side of the equation.
-14 + -1ax + 5x = -1ab + ax + -1ax + -1bx

Combine like terms: ax + -1ax = 0
-14 + -1ax + 5x = -1ab + 0 + -1bx
-14 + -1ax + 5x = -1ab + -1bx

Add 'bx' to each side of the equation.
-14 + -1ax + bx + 5x = -1ab + -1bx + bx

Combine like terms: -1bx + bx = 0
-14 + -1ax + bx + 5x = -1ab + 0
-14 + -1ax + bx + 5x = -1ab

Add '14' to each side of the equation.
-14 + -1ax + bx + 14 + 5x = 14 + -1ab

Reorder the terms:
-14 + 14 + -1ax + bx + 5x = 14 + -1ab

Combine like terms: -14 + 14 = 0
0 + -1ax + bx + 5x = 14 + -1ab
-1ax + bx + 5x = 14 + -1ab

Reorder the terms:
-14 + ab + -1ax + bx + 5x = 14 + -1ab + -14 + ab

Reorder the terms:
-14 + ab + -1ax + bx + 5x = 14 + -14 + -1ab + ab

Combine like terms: 14 + -14 = 0
-14 + ab + -1ax + bx + 5x = 0 + -1ab + ab
-14 + ab + -1ax + bx + 5x = -1ab + ab

Combine like terms: -1ab + ab = 0
-14 + ab + -1ax + bx + 5x = 0

The solution to this equation could not be determined.

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