x(4x-9)=13

Solution for x(4x-9)=13 equation:

Simplifying
x(4x + -9) = 13

Reorder the terms:
x(-9 + 4x) = 13
(-9 * x + 4x * x) = 13
(-9x + 4x2) = 13

Solving
-9x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -9x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -9x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(13 + -4x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {-1, 3.25}