0=60x^2-10x-20

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Solution for 0=60x^2-10x-20 equation: 


Simplifying
0 = 60x2 + -10x + -20

Reorder the terms:
0 = -20 + -10x + 60x2

Solving
0 = -20 + -10x + 60x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + 10x + -60x2 = -20 + -10x + 60x2 + 20 + 10x + -60x2

Reorder the terms:
20 + 10x + -60x2 = -20 + 20 + -10x + 10x + 60x2 + -60x2

Combine like terms: -20 + 20 = 0
20 + 10x + -60x2 = 0 + -10x + 10x + 60x2 + -60x2
20 + 10x + -60x2 = -10x + 10x + 60x2 + -60x2

Combine like terms: -10x + 10x = 0
20 + 10x + -60x2 = 0 + 60x2 + -60x2
20 + 10x + -60x2 = 60x2 + -60x2

Combine like terms: 60x2 + -60x2 = 0
20 + 10x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(2 + x + -6x2) = 0

Factor a trinomial.
10((2 + -3x)(1 + 2x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0.6666666667, -0.5}

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