(4x-6)(2x-5)=0

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Solution for (4x-6)(2x-5)=0 equation: 


Simplifying
(4x + -6)(2x + -5) = 0

Reorder the terms:
(-6 + 4x)(2x + -5) = 0

Reorder the terms:
(-6 + 4x)(-5 + 2x) = 0

Multiply (-6 + 4x) * (-5 + 2x)
(-6(-5 + 2x) + 4x * (-5 + 2x)) = 0
((-5 * -6 + 2x * -6) + 4x * (-5 + 2x)) = 0
((30 + -12x) + 4x * (-5 + 2x)) = 0
(30 + -12x + (-5 * 4x + 2x * 4x)) = 0
(30 + -12x + (-20x + 8x2)) = 0

Combine like terms: -12x + -20x = -32x
(30 + -32x + 8x2) = 0

Solving
30 + -32x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -16x + 4x2) = 0

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

Ignore the factor 2.

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 + -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
Solution
x = {1.5, 2.5}

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