3x^2+4x=10x+45

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Solution for 3x^2+4x=10x+45 equation: 


Simplifying
3x2 + 4x = 10x + 45

Reorder the terms:
4x + 3x2 = 10x + 45

Reorder the terms:
4x + 3x2 = 45 + 10x

Solving
4x + 3x2 = 45 + 10x

Solving for variable 'x'.

Reorder the terms:
-45 + 4x + -10x + 3x2 = 45 + 10x + -45 + -10x

Combine like terms: 4x + -10x = -6x
-45 + -6x + 3x2 = 45 + 10x + -45 + -10x

Reorder the terms:
-45 + -6x + 3x2 = 45 + -45 + 10x + -10x

Combine like terms: 45 + -45 = 0
-45 + -6x + 3x2 = 0 + 10x + -10x
-45 + -6x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-45 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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