2x=5x-25+(x-5)(x-5)

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Solution for 2x=5x-25+(x-5)(x-5) equation: 


Simplifying
2x = 5x + -25 + (x + -5)(x + -5)

Reorder the terms:
2x = 5x + -25 + (-5 + x)(x + -5)

Reorder the terms:
2x = 5x + -25 + (-5 + x)(-5 + x)

Multiply (-5 + x) * (-5 + x)
2x = 5x + -25 + (-5(-5 + x) + x(-5 + x))
2x = 5x + -25 + ((-5 * -5 + x * -5) + x(-5 + x))
2x = 5x + -25 + ((25 + -5x) + x(-5 + x))
2x = 5x + -25 + (25 + -5x + (-5 * x + x * x))
2x = 5x + -25 + (25 + -5x + (-5x + x2))

Combine like terms: -5x + -5x = -10x
2x = 5x + -25 + (25 + -10x + x2)

Reorder the terms:
2x = -25 + 25 + 5x + -10x + x2

Combine like terms: -25 + 25 = 0
2x = 0 + 5x + -10x + x2
2x = 5x + -10x + x2

Combine like terms: 5x + -10x = -5x
2x = -5x + x2

Solving
2x = -5x + x2

Solving for variable 'x'.

Combine like terms: 2x + 5x = 7x
7x + -1x2 = -5x + x2 + 5x + -1x2

Reorder the terms:
7x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
7x + -1x2 = 0 + x2 + -1x2
7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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