12x+35=2x^2+3

Solution for 12x+35=2x^2+3 equation:

Simplifying
12x + 35 = 2x2 + 3

Reorder the terms:
35 + 12x = 2x2 + 3

Reorder the terms:
35 + 12x = 3 + 2x2

Solving
35 + 12x = 3 + 2x2

Solving for variable 'x'.

Reorder the terms:
35 + -3 + 12x + -2x2 = 3 + 2x2 + -3 + -2x2

Combine like terms: 35 + -3 = 32
32 + 12x + -2x2 = 3 + 2x2 + -3 + -2x2

Reorder the terms:
32 + 12x + -2x2 = 3 + -3 + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
32 + 12x + -2x2 = 0 + 2x2 + -2x2
32 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 6x + -1x2) = 0

Factor a trinomial.
2((8 + -1x)(2 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {8, -2}