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

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


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

Reorder the terms:
(-10 + 5x)(6x + 10) = 0

Reorder the terms:
(-10 + 5x)(10 + 6x) = 0

Multiply (-10 + 5x) * (10 + 6x)
(-10(10 + 6x) + 5x * (10 + 6x)) = 0
((10 * -10 + 6x * -10) + 5x * (10 + 6x)) = 0
((-100 + -60x) + 5x * (10 + 6x)) = 0
(-100 + -60x + (10 * 5x + 6x * 5x)) = 0
(-100 + -60x + (50x + 30x2)) = 0

Combine like terms: -60x + 50x = -10x
(-100 + -10x + 30x2) = 0

Solving
-100 + -10x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-10 + -1x + 3x2) = 0

Factor a trinomial.
10((-5 + -3x)(2 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 2}

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