(5x-10)(4x+6)=0

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Solution for (5x-10)(4x+6)=0 equation: 


Simplifying
(5x + -10)(4x + 6) = 0

Reorder the terms:
(-10 + 5x)(4x + 6) = 0

Reorder the terms:
(-10 + 5x)(6 + 4x) = 0

Multiply (-10 + 5x) * (6 + 4x)
(-10(6 + 4x) + 5x * (6 + 4x)) = 0
((6 * -10 + 4x * -10) + 5x * (6 + 4x)) = 0
((-60 + -40x) + 5x * (6 + 4x)) = 0
(-60 + -40x + (6 * 5x + 4x * 5x)) = 0
(-60 + -40x + (30x + 20x2)) = 0

Combine like terms: -40x + 30x = -10x
(-60 + -10x + 20x2) = 0

Solving
-60 + -10x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-6 + -1x + 2x2) = 0

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

Ignore the factor 10.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 2}

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