2x^2-7x+5=(x-1)(x-1)

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Solution for 2x^2-7x+5=(x-1)(x-1) equation: 


Simplifying
2x2 + -7x + 5 = (x + -1)(x + -1)

Reorder the terms:
5 + -7x + 2x2 = (x + -1)(x + -1)

Reorder the terms:
5 + -7x + 2x2 = (-1 + x)(x + -1)

Reorder the terms:
5 + -7x + 2x2 = (-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
5 + -7x + 2x2 = (-1(-1 + x) + x(-1 + x))
5 + -7x + 2x2 = ((-1 * -1 + x * -1) + x(-1 + x))
5 + -7x + 2x2 = ((1 + -1x) + x(-1 + x))
5 + -7x + 2x2 = (1 + -1x + (-1 * x + x * x))
5 + -7x + 2x2 = (1 + -1x + (-1x + x2))

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

Solving
5 + -7x + 2x2 = 1 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
5 + -1 + -7x + 2x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 5 + -1 = 4
4 + -7x + 2x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: -7x + 2x = -5x
4 + -5x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
4 + -5x + 1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
4 + -5x + 1x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
4 + -5x + 1x2 = 0 + -2x + 2x + x2 + -1x2
4 + -5x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
4 + -5x + 1x2 = 0 + x2 + -1x2
4 + -5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -5x + 1x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {1, 4}

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