189=4x^2+6x+9

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Solution for 189=4x^2+6x+9 equation: 


Simplifying
189 = 4x2 + 6x + 9

Reorder the terms:
189 = 9 + 6x + 4x2

Solving
189 = 9 + 6x + 4x2

Solving for variable 'x'.

Combine like terms: 189 + -9 = 180
180 + -6x + -4x2 = 9 + 6x + 4x2 + -9 + -6x + -4x2

Reorder the terms:
180 + -6x + -4x2 = 9 + -9 + 6x + -6x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
180 + -6x + -4x2 = 0 + 6x + -6x + 4x2 + -4x2
180 + -6x + -4x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
180 + -6x + -4x2 = 0 + 4x2 + -4x2
180 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
180 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(90 + -3x + -2x2) = 0

Factor a trinomial.
2((6 + -1x)(15 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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

Simplifying
15 + 2x = 0

Solving
15 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -7.5

Simplifying
x = -7.5
Solution
x = {6, -7.5}

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