72=-16x^2+24x+144

Solution for 72=-16x^2+24x+144 equation:

Simplifying
72 = -16x2 + 24x + 144

Reorder the terms:
72 = 144 + 24x + -16x2

Solving
72 = 144 + 24x + -16x2

Solving for variable 'x'.

Combine like terms: 72 + -144 = -72
-72 + -24x + 16x2 = 144 + 24x + -16x2 + -144 + -24x + 16x2

Reorder the terms:
-72 + -24x + 16x2 = 144 + -144 + 24x + -24x + -16x2 + 16x2

Combine like terms: 144 + -144 = 0
-72 + -24x + 16x2 = 0 + 24x + -24x + -16x2 + 16x2
-72 + -24x + 16x2 = 24x + -24x + -16x2 + 16x2

Combine like terms: 24x + -24x = 0
-72 + -24x + 16x2 = 0 + -16x2 + 16x2
-72 + -24x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-72 + -24x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-9 + -3x + 2x2) = 0

Factor a trinomial.
8((-3 + -2x)(3 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 3}