3x^2+4x=5*2x+9

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Solution for 3x^2+4x=5*2x+9 equation: 


Simplifying
3x2 + 4x = 5 * 2x + 9

Reorder the terms:
4x + 3x2 = 5 * 2x + 9

Multiply 5 * 2
4x + 3x2 = 10x + 9

Reorder the terms:
4x + 3x2 = 9 + 10x

Solving
4x + 3x2 = 9 + 10x

Solving for variable 'x'.

Reorder the terms:
-9 + 4x + -10x + 3x2 = 9 + 10x + -9 + -10x

Combine like terms: 4x + -10x = -6x
-9 + -6x + 3x2 = 9 + 10x + -9 + -10x

Reorder the terms:
-9 + -6x + 3x2 = 9 + -9 + 10x + -10x

Combine like terms: 9 + -9 = 0
-9 + -6x + 3x2 = 0 + 10x + -10x
-9 + -6x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-9 + -6x + 3x2 = 0

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

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

Ignore the factor 3.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}

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