3x^2+10x=42-5x

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Solution for 3x^2+10x=42-5x equation: 


Simplifying
3x2 + 10x = 42 + -5x

Reorder the terms:
10x + 3x2 = 42 + -5x

Solving
10x + 3x2 = 42 + -5x

Solving for variable 'x'.

Reorder the terms:
-42 + 10x + 5x + 3x2 = 42 + -5x + -42 + 5x

Combine like terms: 10x + 5x = 15x
-42 + 15x + 3x2 = 42 + -5x + -42 + 5x

Reorder the terms:
-42 + 15x + 3x2 = 42 + -42 + -5x + 5x

Combine like terms: 42 + -42 = 0
-42 + 15x + 3x2 = 0 + -5x + 5x
-42 + 15x + 3x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-42 + 15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
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
Solution
x = {-7, 2}

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