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

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


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

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

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

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

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

Combine like terms: 3x + -2x = 1x
2 + -5x + 2x2 = (-6 + 1x + x2) + 3x

Reorder the terms:
2 + -5x + 2x2 = -6 + 1x + 3x + x2

Combine like terms: 1x + 3x = 4x
2 + -5x + 2x2 = -6 + 4x + x2

Solving
2 + -5x + 2x2 = -6 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
2 + 6 + -5x + -4x + 2x2 + -1x2 = -6 + 4x + x2 + 6 + -4x + -1x2

Combine like terms: 2 + 6 = 8
8 + -5x + -4x + 2x2 + -1x2 = -6 + 4x + x2 + 6 + -4x + -1x2

Combine like terms: -5x + -4x = -9x
8 + -9x + 2x2 + -1x2 = -6 + 4x + x2 + 6 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
8 + -9x + 1x2 = -6 + 4x + x2 + 6 + -4x + -1x2

Reorder the terms:
8 + -9x + 1x2 = -6 + 6 + 4x + -4x + x2 + -1x2

Combine like terms: -6 + 6 = 0
8 + -9x + 1x2 = 0 + 4x + -4x + x2 + -1x2
8 + -9x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
8 + -9x + 1x2 = 0 + x2 + -1x2
8 + -9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -9x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {1, 8}

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