0=(4x+5)(x-6)

Solution for 0=(4x+5)(x-6) equation:

Simplifying
0 = (4x + 5)(x + -6)

Reorder the terms:
0 = (5 + 4x)(x + -6)

Reorder the terms:
0 = (5 + 4x)(-6 + x)

Multiply (5 + 4x) * (-6 + x)
0 = (5(-6 + x) + 4x * (-6 + x))
0 = ((-6 * 5 + x * 5) + 4x * (-6 + x))
0 = ((-30 + 5x) + 4x * (-6 + x))
0 = (-30 + 5x + (-6 * 4x + x * 4x))
0 = (-30 + 5x + (-24x + 4x2))

Combine like terms: 5x + -24x = -19x
0 = (-30 + -19x + 4x2)

Solving
0 = -30 + -19x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 30 = 30
30 + 19x + -4x2 = -30 + -19x + 4x2 + 30 + 19x + -4x2

Reorder the terms:
30 + 19x + -4x2 = -30 + 30 + -19x + 19x + 4x2 + -4x2

Combine like terms: -30 + 30 = 0
30 + 19x + -4x2 = 0 + -19x + 19x + 4x2 + -4x2
30 + 19x + -4x2 = -19x + 19x + 4x2 + -4x2

Combine like terms: -19x + 19x = 0
30 + 19x + -4x2 = 0 + 4x2 + -4x2
30 + 19x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
30 + 19x + -4x2 = 0

Factor a trinomial.
(6 + -1x)(5 + 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 '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {6, -1.25}