0=(8x-5)(2x-3)

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Solution for 0=(8x-5)(2x-3) equation: 


Simplifying
0 = (8x + -5)(2x + -3)

Reorder the terms:
0 = (-5 + 8x)(2x + -3)

Reorder the terms:
0 = (-5 + 8x)(-3 + 2x)

Multiply (-5 + 8x) * (-3 + 2x)
0 = (-5(-3 + 2x) + 8x * (-3 + 2x))
0 = ((-3 * -5 + 2x * -5) + 8x * (-3 + 2x))
0 = ((15 + -10x) + 8x * (-3 + 2x))
0 = (15 + -10x + (-3 * 8x + 2x * 8x))
0 = (15 + -10x + (-24x + 16x2))

Combine like terms: -10x + -24x = -34x
0 = (15 + -34x + 16x2)

Solving
0 = 15 + -34x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 34x + -16x2 = 15 + -34x + 16x2 + -15 + 34x + -16x2

Reorder the terms:
-15 + 34x + -16x2 = 15 + -15 + -34x + 34x + 16x2 + -16x2

Combine like terms: 15 + -15 = 0
-15 + 34x + -16x2 = 0 + -34x + 34x + 16x2 + -16x2
-15 + 34x + -16x2 = -34x + 34x + 16x2 + -16x2

Combine like terms: -34x + 34x = 0
-15 + 34x + -16x2 = 0 + 16x2 + -16x2
-15 + 34x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-15 + 34x + -16x2 = 0

Factor a trinomial.
(-3 + 2x)(5 + -8x) = 0


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 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 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 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625
Solution
x = {1.5, 0.625}

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