3(x-5)(x-7)=144

Solution for 3(x-5)(x-7)=144 equation:

Simplifying
3(x + -5)(x + -7) = 144

Reorder the terms:
3(-5 + x)(x + -7) = 144

Reorder the terms:
3(-5 + x)(-7 + x) = 144

Multiply (-5 + x) * (-7 + x)
3(-5(-7 + x) + x(-7 + x)) = 144
3((-7 * -5 + x * -5) + x(-7 + x)) = 144
3((35 + -5x) + x(-7 + x)) = 144
3(35 + -5x + (-7 * x + x * x)) = 144
3(35 + -5x + (-7x + x2)) = 144

Combine like terms: -5x + -7x = -12x
3(35 + -12x + x2) = 144
(35 * 3 + -12x * 3 + x2 * 3) = 144
(105 + -36x + 3x2) = 144

Solving
105 + -36x + 3x2 = 144

Solving for variable 'x'.

Reorder the terms:
105 + -144 + -36x + 3x2 = 144 + -144

Combine like terms: 105 + -144 = -39
-39 + -36x + 3x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-39 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + -12x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(13 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-1, 13}