6x^2-4x=10x-4

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Solution for 6x^2-4x=10x-4 equation: 


Simplifying
6x2 + -4x = 10x + -4

Reorder the terms:
-4x + 6x2 = 10x + -4

Reorder the terms:
-4x + 6x2 = -4 + 10x

Solving
-4x + 6x2 = -4 + 10x

Solving for variable 'x'.

Reorder the terms:
4 + -4x + -10x + 6x2 = -4 + 10x + 4 + -10x

Combine like terms: -4x + -10x = -14x
4 + -14x + 6x2 = -4 + 10x + 4 + -10x

Reorder the terms:
4 + -14x + 6x2 = -4 + 4 + 10x + -10x

Combine like terms: -4 + 4 = 0
4 + -14x + 6x2 = 0 + 10x + -10x
4 + -14x + 6x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
4 + -14x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -7x + 3x2) = 0

Factor a trinomial.
2((1 + -3x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.3333333333, 2}

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