4x^2+20x=-24x+48

Solution for 4x^2+20x=-24x+48 equation:

Simplifying
4x2 + 20x = -24x + 48

Reorder the terms:
20x + 4x2 = -24x + 48

Reorder the terms:
20x + 4x2 = 48 + -24x

Solving
20x + 4x2 = 48 + -24x

Solving for variable 'x'.

Reorder the terms:
-48 + 20x + 24x + 4x2 = 48 + -24x + -48 + 24x

Combine like terms: 20x + 24x = 44x
-48 + 44x + 4x2 = 48 + -24x + -48 + 24x

Reorder the terms:
-48 + 44x + 4x2 = 48 + -48 + -24x + 24x

Combine like terms: 48 + -48 = 0
-48 + 44x + 4x2 = 0 + -24x + 24x
-48 + 44x + 4x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-48 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 11x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(1 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 1}