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

Solution for (6+x)(4x-9)=0 equation:

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

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

Multiply (6 + x) * (-9 + 4x)
(6(-9 + 4x) + x(-9 + 4x)) = 0
((-9 * 6 + 4x * 6) + x(-9 + 4x)) = 0
((-54 + 24x) + x(-9 + 4x)) = 0
(-54 + 24x + (-9 * x + 4x * x)) = 0
(-54 + 24x + (-9x + 4x2)) = 0

Combine like terms: 24x + -9x = 15x
(-54 + 15x + 4x2) = 0

Solving
-54 + 15x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(9 + -4x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-6, 2.25}