45x^2+20x=45x+20

Solution for 45x^2+20x=45x+20 equation:

Simplifying
45x2 + 20x = 45x + 20

Reorder the terms:
20x + 45x2 = 45x + 20

Reorder the terms:
20x + 45x2 = 20 + 45x

Solving
20x + 45x2 = 20 + 45x

Solving for variable 'x'.

Reorder the terms:
-20 + 20x + -45x + 45x2 = 20 + 45x + -20 + -45x

Combine like terms: 20x + -45x = -25x
-20 + -25x + 45x2 = 20 + 45x + -20 + -45x

Reorder the terms:
-20 + -25x + 45x2 = 20 + -20 + 45x + -45x

Combine like terms: 20 + -20 = 0
-20 + -25x + 45x2 = 0 + 45x + -45x
-20 + -25x + 45x2 = 45x + -45x

Combine like terms: 45x + -45x = 0
-20 + -25x + 45x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + -5x + 9x2) = 0

Factor a trinomial.
5((-4 + -9x)(1 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9x = 0 + 4

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

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

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444
Subproblem 2
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
Solution
x = {-0.4444444444, 1}