2x^2+10x=4x^2-12

Solution for 2x^2+10x=4x^2-12 equation:

Simplifying
2x2 + 10x = 4x2 + -12

Reorder the terms:
10x + 2x2 = 4x2 + -12

Reorder the terms:
10x + 2x2 = -12 + 4x2

Solving
10x + 2x2 = -12 + 4x2

Solving for variable 'x'.

Reorder the terms:
12 + 10x + 2x2 + -4x2 = -12 + 4x2 + 12 + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
12 + 10x + -2x2 = -12 + 4x2 + 12 + -4x2

Reorder the terms:
12 + 10x + -2x2 = -12 + 12 + 4x2 + -4x2

Combine like terms: -12 + 12 = 0
12 + 10x + -2x2 = 0 + 4x2 + -4x2
12 + 10x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {6, -1}