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

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

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

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

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

Multiply (-3 + 3x) * (3 + 4x)
(-3(3 + 4x) + 3x * (3 + 4x)) = 0
((3 * -3 + 4x * -3) + 3x * (3 + 4x)) = 0
((-9 + -12x) + 3x * (3 + 4x)) = 0
(-9 + -12x + (3 * 3x + 4x * 3x)) = 0
(-9 + -12x + (9x + 12x2)) = 0

Combine like terms: -12x + 9x = -3x
(-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}