6x(x-1)+(-3x-10)+4=0

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Solution for 6x(x-1)+(-3x-10)+4=0 equation: 


Simplifying
6x(x + -1) + (-3x + -10) + 4 = 0

Reorder the terms:
6x(-1 + x) + (-3x + -10) + 4 = 0
(-1 * 6x + x * 6x) + (-3x + -10) + 4 = 0
(-6x + 6x2) + (-3x + -10) + 4 = 0

Reorder the terms:
-6x + 6x2 + (-10 + -3x) + 4 = 0

Remove parenthesis around (-10 + -3x)
-6x + 6x2 + -10 + -3x + 4 = 0

Reorder the terms:
-10 + 4 + -6x + -3x + 6x2 = 0

Combine like terms: -10 + 4 = -6
-6 + -6x + -3x + 6x2 = 0

Combine like terms: -6x + -3x = -9x
-6 + -9x + 6x2 = 0

Solving
-6 + -9x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

Subproblem 1
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

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 = {-0.5, 2}

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