(8x-12)(5x-25)=0

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Solution for (8x-12)(5x-25)=0 equation: 


Simplifying
(8x + -12)(5x + -25) = 0

Reorder the terms:
(-12 + 8x)(5x + -25) = 0

Reorder the terms:
(-12 + 8x)(-25 + 5x) = 0

Multiply (-12 + 8x) * (-25 + 5x)
(-12(-25 + 5x) + 8x * (-25 + 5x)) = 0
((-25 * -12 + 5x * -12) + 8x * (-25 + 5x)) = 0
((300 + -60x) + 8x * (-25 + 5x)) = 0
(300 + -60x + (-25 * 8x + 5x * 8x)) = 0
(300 + -60x + (-200x + 40x2)) = 0

Combine like terms: -60x + -200x = -260x
(300 + -260x + 40x2) = 0

Solving
300 + -260x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(15 + -13x + 2x2) = 0

Factor a trinomial.
20((3 + -2x)(5 + -1x)) = 0

Ignore the factor 20.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.5, 5}

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