4x^2-20x=15x+9

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Solution for 4x^2-20x=15x+9 equation: 


Simplifying
4x2 + -20x = 15x + 9

Reorder the terms:
-20x + 4x2 = 15x + 9

Reorder the terms:
-20x + 4x2 = 9 + 15x

Solving
-20x + 4x2 = 9 + 15x

Solving for variable 'x'.

Reorder the terms:
-9 + -20x + -15x + 4x2 = 9 + 15x + -9 + -15x

Combine like terms: -20x + -15x = -35x
-9 + -35x + 4x2 = 9 + 15x + -9 + -15x

Reorder the terms:
-9 + -35x + 4x2 = 9 + -9 + 15x + -15x

Combine like terms: 9 + -9 = 0
-9 + -35x + 4x2 = 0 + 15x + -15x
-9 + -35x + 4x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-9 + -35x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.25, 9}

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