(x-9)(4x+3)=0

Solution for (x-9)(4x+3)=0 equation:

Simplifying
(x + -9)(4x + 3) = 0

Reorder the terms:
(-9 + x)(4x + 3) = 0

Reorder the terms:
(-9 + x)(3 + 4x) = 0

Multiply (-9 + x) * (3 + 4x)
(-9(3 + 4x) + x(3 + 4x)) = 0
((3 * -9 + 4x * -9) + x(3 + 4x)) = 0
((-27 + -36x) + x(3 + 4x)) = 0
(-27 + -36x + (3 * x + 4x * x)) = 0
(-27 + -36x + (3x + 4x2)) = 0

Combine like terms: -36x + 3x = -33x
(-27 + -33x + 4x2) = 0

Solving
-27 + -33x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -4x)(9 + -1x) = 0

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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.75, 9}