10x(6x-4)-5(6x-4)=0

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Solution for 10x(6x-4)-5(6x-4)=0 equation: 


Simplifying
10x(6x + -4) + -5(6x + -4) = 0

Reorder the terms:
10x(-4 + 6x) + -5(6x + -4) = 0
(-4 * 10x + 6x * 10x) + -5(6x + -4) = 0
(-40x + 60x2) + -5(6x + -4) = 0

Reorder the terms:
-40x + 60x2 + -5(-4 + 6x) = 0
-40x + 60x2 + (-4 * -5 + 6x * -5) = 0
-40x + 60x2 + (20 + -30x) = 0

Reorder the terms:
20 + -40x + -30x + 60x2 = 0

Combine like terms: -40x + -30x = -70x
20 + -70x + 60x2 = 0

Solving
20 + -70x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(2 + -7x + 6x2) = 0

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

Ignore the factor 10.

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 + -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
Solution
x = {0.5, 0.6666666667}

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