0=(13-0.25x)(12+4x)

Solution for 0=(13-0.25x)(12+4x) equation:

Simplifying
0 = (13 + -0.25x)(12 + 4x)

Multiply (13 + -0.25x) * (12 + 4x)
0 = (13(12 + 4x) + -0.25x * (12 + 4x))
0 = ((12 * 13 + 4x * 13) + -0.25x * (12 + 4x))
0 = ((156 + 52x) + -0.25x * (12 + 4x))
0 = (156 + 52x + (12 * -0.25x + 4x * -0.25x))
0 = (156 + 52x + (-3x + -1x2))

Combine like terms: 52x + -3x = 49x
0 = (156 + 49x + -1x2)

Solving
0 = 156 + 49x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -156 = -156
-156 + -49x + x2 = 156 + 49x + -1x2 + -156 + -49x + x2

Reorder the terms:
-156 + -49x + x2 = 156 + -156 + 49x + -49x + -1x2 + x2

Combine like terms: 156 + -156 = 0
-156 + -49x + x2 = 0 + 49x + -49x + -1x2 + x2
-156 + -49x + x2 = 49x + -49x + -1x2 + x2

Combine like terms: 49x + -49x = 0
-156 + -49x + x2 = 0 + -1x2 + x2
-156 + -49x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-156 + -49x + x2 = 0

Factor a trinomial.
(-3 + -1x)(52 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(52 + -1x)' equal to zero and attempt to solve:

Simplifying
52 + -1x = 0

Solving
52 + -1x = 0

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

Add '-52' to each side of the equation.
52 + -52 + -1x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -1x = 0 + -52
-1x = 0 + -52

Combine like terms: 0 + -52 = -52
-1x = -52

Divide each side by '-1'.
x = 52

Simplifying
x = 52
Solution
x = {-3, 52}