3(4x+3)(x-1)=0

Solution for 3(4x+3)(x-1)=0 equation:

Simplifying
3(4x + 3)(x + -1) = 0

Reorder the terms:
3(3 + 4x)(x + -1) = 0

Reorder the terms:
3(3 + 4x)(-1 + x) = 0

Multiply (3 + 4x) * (-1 + x)
3(3(-1 + x) + 4x * (-1 + x)) = 0
3((-1 * 3 + x * 3) + 4x * (-1 + x)) = 0
3((-3 + 3x) + 4x * (-1 + x)) = 0
3(-3 + 3x + (-1 * 4x + x * 4x)) = 0
3(-3 + 3x + (-4x + 4x2)) = 0

Combine like terms: 3x + -4x = -1x
3(-3 + -1x + 4x2) = 0
(-3 * 3 + -1x * 3 + 4x2 * 3) = 0
(-9 + -3x + 12x2) = 0

Solving
-9 + -3x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1x + 4x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

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

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

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, 1}