9x^2-20x+16=4x+9

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Solution for 9x^2-20x+16=4x+9 equation: 


Simplifying
9x2 + -20x + 16 = 4x + 9

Reorder the terms:
16 + -20x + 9x2 = 4x + 9

Reorder the terms:
16 + -20x + 9x2 = 9 + 4x

Solving
16 + -20x + 9x2 = 9 + 4x

Solving for variable 'x'.

Reorder the terms:
16 + -9 + -20x + -4x + 9x2 = 9 + 4x + -9 + -4x

Combine like terms: 16 + -9 = 7
7 + -20x + -4x + 9x2 = 9 + 4x + -9 + -4x

Combine like terms: -20x + -4x = -24x
7 + -24x + 9x2 = 9 + 4x + -9 + -4x

Reorder the terms:
7 + -24x + 9x2 = 9 + -9 + 4x + -4x

Combine like terms: 9 + -9 = 0
7 + -24x + 9x2 = 0 + 4x + -4x
7 + -24x + 9x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
7 + -24x + 9x2 = 0

Factor a trinomial.
(1 + -3x)(7 + -3x) = 0


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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0.3333333333, 2.333333333}

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