(5x-10)(-3x-12)=0

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Solution for (5x-10)(-3x-12)=0 equation: 


Simplifying
(5x + -10)(-3x + -12) = 0

Reorder the terms:
(-10 + 5x)(-3x + -12) = 0

Reorder the terms:
(-10 + 5x)(-12 + -3x) = 0

Multiply (-10 + 5x) * (-12 + -3x)
(-10(-12 + -3x) + 5x * (-12 + -3x)) = 0
((-12 * -10 + -3x * -10) + 5x * (-12 + -3x)) = 0
((120 + 30x) + 5x * (-12 + -3x)) = 0
(120 + 30x + (-12 * 5x + -3x * 5x)) = 0
(120 + 30x + (-60x + -15x2)) = 0

Combine like terms: 30x + -60x = -30x
(120 + -30x + -15x2) = 0

Solving
120 + -30x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(8 + -2x + -1x2) = 0

Factor a trinomial.
15((2 + -1x)(4 + x)) = 0

Ignore the factor 15.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {2, -4}

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