ようではないか is a construction that will primarily be used for making suggestions for mutual activities. This is a combination of either of the auxiliary verbs う or よう, ではない, and the sentence-ending particle, か. う and よう primarily express will or intent like ‘shall’ in English. Due to the negation following them, the literal translation will be similar to ‘shall we not do (A)?’. For ease of translation, this structure can be remembered as simply ‘let’s do (A)’, or ‘why don’t we do (A)’.
As with all structures that use う or よう, ようではないか will be attached to the end of a verb indicating the action which is being suggested.

• 正々（せいせい）堂々（どうどう）と戦（たたか）おうではないか。
  Why don’t we fight fair and square?
• この問題（もんだい）をどう解決（かいけつ）するかみんなで考（かんが）えようではないか。
  Why don’t we all think about how we can solve this problem?

Alternatively, the abbreviated for of じゃない may be used in place of ではない.

• こういう時（とき）こそお互（たが）い助（たす）け合（あ）おうじゃないか。
  Why don’t we help each other, especially in times like this.
• せっかく日本（にほん）に来（き）たのだから、食（た）べれるだけの日本食（にほんしょく）を食（た）べようじゃないか。
  Since we have come all the way to Japan, why don't we eat as much Japanese food as we can.

Despite this, ようではないか is primarily a formal grammar structure, so will most often use the unabbreviated version, or even more polite ようではありませんか construction.