16x^2-24x+9=25x^2

Solution for 16x^2-24x+9=25x^2 equation:

Simplifying
16x2 + -24x + 9 = 25x2

Reorder the terms:
9 + -24x + 16x2 = 25x2

Solving
9 + -24x + 16x2 = 25x2

Solving for variable 'x'.

Combine like terms: 16x2 + -25x2 = -9x2
9 + -24x + -9x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
9 + -24x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -8x + -3x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {0.3333333333, -3}