5x^2-18x+4=12x+39

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Solution for 5x^2-18x+4=12x+39 equation: 


Simplifying
5x2 + -18x + 4 = 12x + 39

Reorder the terms:
4 + -18x + 5x2 = 12x + 39

Reorder the terms:
4 + -18x + 5x2 = 39 + 12x

Solving
4 + -18x + 5x2 = 39 + 12x

Solving for variable 'x'.

Reorder the terms:
4 + -39 + -18x + -12x + 5x2 = 39 + 12x + -39 + -12x

Combine like terms: 4 + -39 = -35
-35 + -18x + -12x + 5x2 = 39 + 12x + -39 + -12x

Combine like terms: -18x + -12x = -30x
-35 + -30x + 5x2 = 39 + 12x + -39 + -12x

Reorder the terms:
-35 + -30x + 5x2 = 39 + -39 + 12x + -12x

Combine like terms: 39 + -39 = 0
-35 + -30x + 5x2 = 0 + 12x + -12x
-35 + -30x + 5x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-35 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -6x + x2) = 0

Factor a trinomial.
5((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 5.

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 '(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
Solution
x = {-1, 7}

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