3x^2-10x+5=-4x+2

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Solution for 3x^2-10x+5=-4x+2 equation: 


Simplifying
3x2 + -10x + 5 = -4x + 2

Reorder the terms:
5 + -10x + 3x2 = -4x + 2

Reorder the terms:
5 + -10x + 3x2 = 2 + -4x

Solving
5 + -10x + 3x2 = 2 + -4x

Solving for variable 'x'.

Reorder the terms:
5 + -2 + -10x + 4x + 3x2 = 2 + -4x + -2 + 4x

Combine like terms: 5 + -2 = 3
3 + -10x + 4x + 3x2 = 2 + -4x + -2 + 4x

Combine like terms: -10x + 4x = -6x
3 + -6x + 3x2 = 2 + -4x + -2 + 4x

Reorder the terms:
3 + -6x + 3x2 = 2 + -2 + -4x + 4x

Combine like terms: 2 + -2 = 0
3 + -6x + 3x2 = 0 + -4x + 4x
3 + -6x + 3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
3 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2x + x2) = 0

Factor a trinomial.
3((1 + -1x)(1 + -1x)) = 0

Ignore the factor 3.

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 '(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 = {1, 1}

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