(3x-6)(8x+10)=0

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Solution for (3x-6)(8x+10)=0 equation: 


Simplifying
(3x + -6)(8x + 10) = 0

Reorder the terms:
(-6 + 3x)(8x + 10) = 0

Reorder the terms:
(-6 + 3x)(10 + 8x) = 0

Multiply (-6 + 3x) * (10 + 8x)
(-6(10 + 8x) + 3x * (10 + 8x)) = 0
((10 * -6 + 8x * -6) + 3x * (10 + 8x)) = 0
((-60 + -48x) + 3x * (10 + 8x)) = 0
(-60 + -48x + (10 * 3x + 8x * 3x)) = 0
(-60 + -48x + (30x + 24x2)) = 0

Combine like terms: -48x + 30x = -18x
(-60 + -18x + 24x2) = 0

Solving
-60 + -18x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-10 + -3x + 4x2) = 0

Factor a trinomial.
6((-5 + -4x)(2 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

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 = {-1.25, 2}

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