3(x-3)4(4x-5)=

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

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

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

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

Reorder the terms for easier multiplication:
3 * 4(-3 + x)(-5 + 4x) = 0

Multiply 3 * 4
12(-3 + x)(-5 + 4x) = 0

Multiply (-3 + x) * (-5 + 4x)
12(-3(-5 + 4x) + x(-5 + 4x)) = 0
12((-5 * -3 + 4x * -3) + x(-5 + 4x)) = 0
12((15 + -12x) + x(-5 + 4x)) = 0
12(15 + -12x + (-5 * x + 4x * x)) = 0
12(15 + -12x + (-5x + 4x2)) = 0

Combine like terms: -12x + -5x = -17x
12(15 + -17x + 4x2) = 0
(15 * 12 + -17x * 12 + 4x2 * 12) = 0
(180 + -204x + 48x2) = 0

Solving
180 + -204x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(15 + -17x + 4x2) = 0

Factor a trinomial.
12((5 + -4x)(3 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.25, 3}