6=2x^2+5x-12

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Solution for 6=2x^2+5x-12 equation: 


Simplifying
6 = 2x2 + 5x + -12

Reorder the terms:
6 = -12 + 5x + 2x2

Solving
6 = -12 + 5x + 2x2

Solving for variable 'x'.

Combine like terms: 6 + 12 = 18
18 + -5x + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Reorder the terms:
18 + -5x + -2x2 = -12 + 12 + 5x + -5x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
18 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
18 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
18 + -5x + -2x2 = 0 + 2x2 + -2x2
18 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + -5x + -2x2 = 0

Factor a trinomial.
(2 + -1x)(9 + 2x) = 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 '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {2, -4.5}

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