4(x+2)(x+5)=280

Solution for 4(x+2)(x+5)=280 equation:

Simplifying
4(x + 2)(x + 5) = 280

Reorder the terms:
4(2 + x)(x + 5) = 280

Reorder the terms:
4(2 + x)(5 + x) = 280

Multiply (2 + x) * (5 + x)
4(2(5 + x) + x(5 + x)) = 280
4((5 * 2 + x * 2) + x(5 + x)) = 280
4((10 + 2x) + x(5 + x)) = 280
4(10 + 2x + (5 * x + x * x)) = 280
4(10 + 2x + (5x + x2)) = 280

Combine like terms: 2x + 5x = 7x
4(10 + 7x + x2) = 280
(10 * 4 + 7x * 4 + x2 * 4) = 280
(40 + 28x + 4x2) = 280

Solving
40 + 28x + 4x2 = 280

Solving for variable 'x'.

Reorder the terms:
40 + -280 + 28x + 4x2 = 280 + -280

Combine like terms: 40 + -280 = -240
-240 + 28x + 4x2 = 280 + -280

Combine like terms: 280 + -280 = 0
-240 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 7x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-12, 5}