x^2+(a+b)x+ab=(x+a)(x+b)

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Solution for x^2+(a+b)x+ab=(x+a)(x+b) equation: 


Simplifying
x2 + (a + b) * x + ab = (x + a)(x + b)

Reorder the terms for easier multiplication:
x2 + x(a + b) + ab = (x + a)(x + b)
x2 + (a * x + b * x) + ab = (x + a)(x + b)
x2 + (ax + bx) + ab = (x + a)(x + b)

Reorder the terms:
ab + ax + bx + x2 = (x + a)(x + b)

Reorder the terms:
ab + ax + bx + x2 = (a + x)(x + b)

Reorder the terms:
ab + ax + bx + x2 = (a + x)(b + x)

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

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

Reorder the terms:
ab + -1ab + ax + bx + x2 = ab + ax + bx + -1ab + x2

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

Reorder the terms:
ax + bx + x2 = ab + -1ab + ax + bx + x2

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

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

Reorder the terms:
ax + -1ax + bx + x2 = ax + bx + -1ax + x2

Combine like terms: ax + -1ax = 0
0 + bx + x2 = ax + bx + -1ax + x2
bx + x2 = ax + bx + -1ax + x2

Reorder the terms:
bx + x2 = ax + -1ax + bx + x2

Combine like terms: ax + -1ax = 0
bx + x2 = 0 + bx + x2
bx + x2 = bx + x2

Add '-1bx' to each side of the equation.
bx + -1bx + x2 = bx + -1bx + x2

Combine like terms: bx + -1bx = 0
0 + x2 = bx + -1bx + x2
x2 = bx + -1bx + x2

Combine like terms: bx + -1bx = 0
x2 = 0 + x2
x2 = x2

Add '-1x2' to each side of the equation.
x2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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