(4x+10)(3x-6)=0

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Solution for (4x+10)(3x-6)=0 equation: 


Simplifying
(4x + 10)(3x + -6) = 0

Reorder the terms:
(10 + 4x)(3x + -6) = 0

Reorder the terms:
(10 + 4x)(-6 + 3x) = 0

Multiply (10 + 4x) * (-6 + 3x)
(10(-6 + 3x) + 4x * (-6 + 3x)) = 0
((-6 * 10 + 3x * 10) + 4x * (-6 + 3x)) = 0
((-60 + 30x) + 4x * (-6 + 3x)) = 0
(-60 + 30x + (-6 * 4x + 3x * 4x)) = 0
(-60 + 30x + (-24x + 12x2)) = 0

Combine like terms: 30x + -24x = 6x
(-60 + 6x + 12x2) = 0

Solving
-60 + 6x + 12x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 6.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 2}

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