0=(3x-4)(-6x+5)

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Solution for 0=(3x-4)(-6x+5) equation: 


Simplifying
0 = (3x + -4)(-6x + 5)

Reorder the terms:
0 = (-4 + 3x)(-6x + 5)

Reorder the terms:
0 = (-4 + 3x)(5 + -6x)

Multiply (-4 + 3x) * (5 + -6x)
0 = (-4(5 + -6x) + 3x * (5 + -6x))
0 = ((5 * -4 + -6x * -4) + 3x * (5 + -6x))
0 = ((-20 + 24x) + 3x * (5 + -6x))
0 = (-20 + 24x + (5 * 3x + -6x * 3x))
0 = (-20 + 24x + (15x + -18x2))

Combine like terms: 24x + 15x = 39x
0 = (-20 + 39x + -18x2)

Solving
0 = -20 + 39x + -18x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -39x + 18x2 = -20 + 39x + -18x2 + 20 + -39x + 18x2

Reorder the terms:
20 + -39x + 18x2 = -20 + 20 + 39x + -39x + -18x2 + 18x2

Combine like terms: -20 + 20 = 0
20 + -39x + 18x2 = 0 + 39x + -39x + -18x2 + 18x2
20 + -39x + 18x2 = 39x + -39x + -18x2 + 18x2

Combine like terms: 39x + -39x = 0
20 + -39x + 18x2 = 0 + -18x2 + 18x2
20 + -39x + 18x2 = -18x2 + 18x2

Combine like terms: -18x2 + 18x2 = 0
20 + -39x + 18x2 = 0

Factor a trinomial.
(5 + -6x)(4 + -3x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0.8333333333, 1.333333333}

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