32x^2=20x-3

Solution for 32x^2=20x-3 equation:

Simplifying
32x2 = 20x + -3

Reorder the terms:
32x2 = -3 + 20x

Solving
32x2 = -3 + 20x

Solving for variable 'x'.

Reorder the terms:
3 + -20x + 32x2 = -3 + 20x + 3 + -20x

Reorder the terms:
3 + -20x + 32x2 = -3 + 3 + 20x + -20x

Combine like terms: -3 + 3 = 0
3 + -20x + 32x2 = 0 + 20x + -20x
3 + -20x + 32x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
3 + -20x + 32x2 = 0

Factor a trinomial.
(1 + -4x)(3 + -8x) = 0

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 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 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {0.25, 0.375}