2x^2-5x+2=(x-3)(x-2)+3

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Solution for 2x^2-5x+2=(x-3)(x-2)+3 equation: 


Simplifying
2x2 + -5x + 2 = (x + -3)(x + -2) + 3

Reorder the terms:
2 + -5x + 2x2 = (x + -3)(x + -2) + 3

Reorder the terms:
2 + -5x + 2x2 = (-3 + x)(x + -2) + 3

Reorder the terms:
2 + -5x + 2x2 = (-3 + x)(-2 + x) + 3

Multiply (-3 + x) * (-2 + x)
2 + -5x + 2x2 = (-3(-2 + x) + x(-2 + x)) + 3
2 + -5x + 2x2 = ((-2 * -3 + x * -3) + x(-2 + x)) + 3
2 + -5x + 2x2 = ((6 + -3x) + x(-2 + x)) + 3
2 + -5x + 2x2 = (6 + -3x + (-2 * x + x * x)) + 3
2 + -5x + 2x2 = (6 + -3x + (-2x + x2)) + 3

Combine like terms: -3x + -2x = -5x
2 + -5x + 2x2 = (6 + -5x + x2) + 3

Reorder the terms:
2 + -5x + 2x2 = 6 + 3 + -5x + x2

Combine like terms: 6 + 3 = 9
2 + -5x + 2x2 = 9 + -5x + x2

Add '5x' to each side of the equation.
2 + -5x + 5x + 2x2 = 9 + -5x + 5x + x2

Combine like terms: -5x + 5x = 0
2 + 0 + 2x2 = 9 + -5x + 5x + x2
2 + 2x2 = 9 + -5x + 5x + x2

Combine like terms: -5x + 5x = 0
2 + 2x2 = 9 + 0 + x2
2 + 2x2 = 9 + x2

Solving
2 + 2x2 = 9 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
2 + 2x2 + -1x2 = 9 + x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
2 + 1x2 = 9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 1x2 = 9 + 0
2 + 1x2 = 9

Add '-2' to each side of the equation.
2 + -2 + 1x2 = 9 + -2

Combine like terms: 2 + -2 = 0
0 + 1x2 = 9 + -2
1x2 = 9 + -2

Combine like terms: 9 + -2 = 7
1x2 = 7

Divide each side by '1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}

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