0=12x^2-52x+40

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Solution for 0=12x^2-52x+40 equation: 


Simplifying
0 = 12x2 + -52x + 40

Reorder the terms:
0 = 40 + -52x + 12x2

Solving
0 = 40 + -52x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + 52x + -12x2 = 40 + -52x + 12x2 + -40 + 52x + -12x2

Reorder the terms:
-40 + 52x + -12x2 = 40 + -40 + -52x + 52x + 12x2 + -12x2

Combine like terms: 40 + -40 = 0
-40 + 52x + -12x2 = 0 + -52x + 52x + 12x2 + -12x2
-40 + 52x + -12x2 = -52x + 52x + 12x2 + -12x2

Combine like terms: -52x + 52x = 0
-40 + 52x + -12x2 = 0 + 12x2 + -12x2
-40 + 52x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-40 + 52x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 13x + -3x2) = 0

Factor a trinomial.
4((-10 + 3x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 3x)' equal to zero and attempt to solve:

Simplifying
-10 + 3x = 0

Solving
-10 + 3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = 0 + 10
3x = 0 + 10

Combine like terms: 0 + 10 = 10
3x = 10

Divide each side by '3'.
x = 3.333333333

Simplifying
x = 3.333333333

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 = {3.333333333, 1}

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