3x^2+12x-61=2

Solution for 3x^2+12x-61=2 equation:

Simplifying
3x2 + 12x + -61 = 2

Reorder the terms:
-61 + 12x + 3x2 = 2

Solving
-61 + 12x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
-61 + -2 + 12x + 3x2 = 2 + -2

Combine like terms: -61 + -2 = -63
-63 + 12x + 3x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-63 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 4x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(3 + -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 '(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
Solution
x = {-7, 3}