45x^2+27x-2=(3x+2)

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Solution for 45x^2+27x-2=(3x+2) equation: 


Simplifying
45x2 + 27x + -2 = (3x + 2)

Reorder the terms:
-2 + 27x + 45x2 = (3x + 2)

Reorder the terms:
-2 + 27x + 45x2 = (2 + 3x)

Remove parenthesis around (2 + 3x)
-2 + 27x + 45x2 = 2 + 3x

Solving
-2 + 27x + 45x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
-2 + -2 + 27x + -3x + 45x2 = 2 + 3x + -2 + -3x

Combine like terms: -2 + -2 = -4
-4 + 27x + -3x + 45x2 = 2 + 3x + -2 + -3x

Combine like terms: 27x + -3x = 24x
-4 + 24x + 45x2 = 2 + 3x + -2 + -3x

Reorder the terms:
-4 + 24x + 45x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
-4 + 24x + 45x2 = 0 + 3x + -3x
-4 + 24x + 45x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + 24x + 45x2 = 0

Factor a trinomial.
(-2 + -3x)(2 + -15x) = 0


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(2 + -15x)' equal to zero and attempt to solve:

Simplifying
2 + -15x = 0

Solving
2 + -15x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -15x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -15x = 0 + -2
-15x = 0 + -2

Combine like terms: 0 + -2 = -2
-15x = -2

Divide each side by '-15'.
x = 0.1333333333

Simplifying
x = 0.1333333333
Solution
x = {-0.6666666667, 0.1333333333}

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