15x^2+45x-9=4x-5x^2

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Solution for 15x^2+45x-9=4x-5x^2 equation: 


Simplifying
15x2 + 45x + -9 = 4x + -5x2

Reorder the terms:
-9 + 45x + 15x2 = 4x + -5x2

Solving
-9 + 45x + 15x2 = 4x + -5x2

Solving for variable 'x'.

Reorder the terms:
-9 + 45x + -4x + 15x2 + 5x2 = 4x + -5x2 + -4x + 5x2

Combine like terms: 45x + -4x = 41x
-9 + 41x + 15x2 + 5x2 = 4x + -5x2 + -4x + 5x2

Combine like terms: 15x2 + 5x2 = 20x2
-9 + 41x + 20x2 = 4x + -5x2 + -4x + 5x2

Reorder the terms:
-9 + 41x + 20x2 = 4x + -4x + -5x2 + 5x2

Combine like terms: 4x + -4x = 0
-9 + 41x + 20x2 = 0 + -5x2 + 5x2
-9 + 41x + 20x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-9 + 41x + 20x2 = 0

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


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

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

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

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

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

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-2.25, 0.2}

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