9x^2=25x-16

Solution for 9x^2=25x-16 equation:

Simplifying
9x2 = 25x + -16

Reorder the terms:
9x2 = -16 + 25x

Solving
9x2 = -16 + 25x

Solving for variable 'x'.

Reorder the terms:
16 + -25x + 9x2 = -16 + 25x + 16 + -25x

Reorder the terms:
16 + -25x + 9x2 = -16 + 16 + 25x + -25x

Combine like terms: -16 + 16 = 0
16 + -25x + 9x2 = 0 + 25x + -25x
16 + -25x + 9x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
16 + -25x + 9x2 = 0

Factor a trinomial.
(1 + -1x)(16 + -9x) = 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 '(16 + -9x)' equal to zero and attempt to solve:

Simplifying
16 + -9x = 0

Solving
16 + -9x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -9x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9x = 0 + -16
-9x = 0 + -16

Combine like terms: 0 + -16 = -16
-9x = -16

Divide each side by '-9'.
x = 1.777777778

Simplifying
x = 1.777777778
Solution
x = {1, 1.777777778}