5(4x^2+12x+9)=80

Solution for 5(4x^2+12x+9)=80 equation:

Simplifying
5(4x2 + 12x + 9) = 80

Reorder the terms:
5(9 + 12x + 4x2) = 80
(9 * 5 + 12x * 5 + 4x2 * 5) = 80
(45 + 60x + 20x2) = 80

Solving
45 + 60x + 20x2 = 80

Solving for variable 'x'.

Reorder the terms:
45 + -80 + 60x + 20x2 = 80 + -80

Combine like terms: 45 + -80 = -35
-35 + 60x + 20x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-35 + 60x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + 12x + 4x2) = 0

Factor a trinomial.
5((-7 + -2x)(1 + -2x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3.5, 0.5}