4x^2+6x-9=3x+1

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Solution for 4x^2+6x-9=3x+1 equation: 


Simplifying
4x2 + 6x + -9 = 3x + 1

Reorder the terms:
-9 + 6x + 4x2 = 3x + 1

Reorder the terms:
-9 + 6x + 4x2 = 1 + 3x

Solving
-9 + 6x + 4x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -1 + 6x + -3x + 4x2 = 1 + 3x + -1 + -3x

Combine like terms: -9 + -1 = -10
-10 + 6x + -3x + 4x2 = 1 + 3x + -1 + -3x

Combine like terms: 6x + -3x = 3x
-10 + 3x + 4x2 = 1 + 3x + -1 + -3x

Reorder the terms:
-10 + 3x + 4x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
-10 + 3x + 4x2 = 0 + 3x + -3x
-10 + 3x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + 3x + 4x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -4x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-2, 1.25}

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