2x^2-7x+21=(x-5)(x-5)

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Solution for 2x^2-7x+21=(x-5)(x-5) equation: 


Simplifying
2x2 + -7x + 21 = (x + -5)(x + -5)

Reorder the terms:
21 + -7x + 2x2 = (x + -5)(x + -5)

Reorder the terms:
21 + -7x + 2x2 = (-5 + x)(x + -5)

Reorder the terms:
21 + -7x + 2x2 = (-5 + x)(-5 + x)

Multiply (-5 + x) * (-5 + x)
21 + -7x + 2x2 = (-5(-5 + x) + x(-5 + x))
21 + -7x + 2x2 = ((-5 * -5 + x * -5) + x(-5 + x))
21 + -7x + 2x2 = ((25 + -5x) + x(-5 + x))
21 + -7x + 2x2 = (25 + -5x + (-5 * x + x * x))
21 + -7x + 2x2 = (25 + -5x + (-5x + x2))

Combine like terms: -5x + -5x = -10x
21 + -7x + 2x2 = (25 + -10x + x2)

Solving
21 + -7x + 2x2 = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
21 + -25 + -7x + 10x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 21 + -25 = -4
-4 + -7x + 10x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -7x + 10x = 3x
-4 + 3x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + 3x + 1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-4 + 3x + 1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-4 + 3x + 1x2 = 0 + -10x + 10x + x2 + -1x2
-4 + 3x + 1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-4 + 3x + 1x2 = 0 + x2 + -1x2
-4 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}

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