(7x+37)(2x-12)=0

Solution for (7x+37)(2x-12)=0 equation:

Simplifying
(7x + 37)(2x + -12) = 0

Reorder the terms:
(37 + 7x)(2x + -12) = 0

Reorder the terms:
(37 + 7x)(-12 + 2x) = 0

Multiply (37 + 7x) * (-12 + 2x)
(37(-12 + 2x) + 7x * (-12 + 2x)) = 0
((-12 * 37 + 2x * 37) + 7x * (-12 + 2x)) = 0
((-444 + 74x) + 7x * (-12 + 2x)) = 0
(-444 + 74x + (-12 * 7x + 2x * 7x)) = 0
(-444 + 74x + (-84x + 14x2)) = 0

Combine like terms: 74x + -84x = -10x
(-444 + -10x + 14x2) = 0

Solving
-444 + -10x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-222 + -5x + 7x2) = 0

Factor a trinomial.
2((-37 + -7x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-37 + -7x)' equal to zero and attempt to solve:

Simplifying
-37 + -7x = 0

Solving
-37 + -7x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -7x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -7x = 0 + 37
-7x = 0 + 37

Combine like terms: 0 + 37 = 37
-7x = 37

Divide each side by '-7'.
x = -5.285714286

Simplifying
x = -5.285714286
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-5.285714286, 6}