(2x-10)(3x+1)=0

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Solution for (2x-10)(3x+1)=0 equation: 


Simplifying
(2x + -10)(3x + 1) = 0

Reorder the terms:
(-10 + 2x)(3x + 1) = 0

Reorder the terms:
(-10 + 2x)(1 + 3x) = 0

Multiply (-10 + 2x) * (1 + 3x)
(-10(1 + 3x) + 2x * (1 + 3x)) = 0
((1 * -10 + 3x * -10) + 2x * (1 + 3x)) = 0
((-10 + -30x) + 2x * (1 + 3x)) = 0
(-10 + -30x + (1 * 2x + 3x * 2x)) = 0
(-10 + -30x + (2x + 6x2)) = 0

Combine like terms: -30x + 2x = -28x
(-10 + -28x + 6x2) = 0

Solving
-10 + -28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -14x + 3x2) = 0

Factor a trinomial.
2((-1 + -3x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.3333333333, 5}

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