6x^2-13x+4=-5x+2

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Solution for 6x^2-13x+4=-5x+2 equation: 


Simplifying
6x2 + -13x + 4 = -5x + 2

Reorder the terms:
4 + -13x + 6x2 = -5x + 2

Reorder the terms:
4 + -13x + 6x2 = 2 + -5x

Solving
4 + -13x + 6x2 = 2 + -5x

Solving for variable 'x'.

Reorder the terms:
4 + -2 + -13x + 5x + 6x2 = 2 + -5x + -2 + 5x

Combine like terms: 4 + -2 = 2
2 + -13x + 5x + 6x2 = 2 + -5x + -2 + 5x

Combine like terms: -13x + 5x = -8x
2 + -8x + 6x2 = 2 + -5x + -2 + 5x

Reorder the terms:
2 + -8x + 6x2 = 2 + -2 + -5x + 5x

Combine like terms: 2 + -2 = 0
2 + -8x + 6x2 = 0 + -5x + 5x
2 + -8x + 6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
2 + -8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -4x + 3x2) = 0

Factor a trinomial.
2((1 + -3x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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 = {0.3333333333, 1}

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